Jesus death by crucifixion is an undisputed fact.
This is attested by Christian and Non Christian sources.
Multiple Attestation
Firstly, Jesus’ death by crucifixion is multiply attested, by a fair number of ancient sources, both Christian and non-Christian alike.
In regards to Christian sources which mention his death, I list from the first century AD all four canonical Gospels, Acts, Paul’s Epistles, all within the Bible; then Ignatius’ Epistles (dating around 110 AD, for example, his Letter to the Symrnaeans, chapters 1 and 2). Many, if not all, of these sources are independent.
Here’s one example I focused on recently in preaching through Mark (usually dated as the earliest Gospel). The narrative in Mark 15:44-45 makes it clear Jesus really was dead. The history books record that men who were crucified sometimes took two or three days to die. A more rapid death was unusual. So in this case, the governor Pilate gets the expert executioner to confirm the death certificate! The observation that Roman centurions were professional soldiers and didn’t make mistakes is well taken. So satisfied, Pilate permitted the body of Jesus to be buried.
By the way, there was a very low probability of surviving execution by crucifixion. Apparently there is only one extant account (in Josephus) of one person surviving crucifixion out of the hundreds reported in ancient literature. (And that case was only when excellent medical care was immediately provided by the Romans, and even so, only one out of three who were so rescued actually survived!)
Criterion of Embarrassment
Mark also stresses that it was women who witnessed the events: death, burial and empty tomb. And each time, verbs of seeing are emphasized. And each time, some of them are named. Mark 15:40 says that when Jesus has just died, at least three women are there. Two of these same women witnessed the burial (Mark 15:47). And in Mark 16:1, all three women are again mentioned as arriving back at the tomb on resurrection Sunday. The appeal to these women’s role as eyewitnesses couldn’t be clearer.
And notice how Mark reports only two of the three are at the burial? Presumably because that’s how it was. Mark wasn’t going to exaggerate. This precision shows a real concern for accuracy.
And presumably these people are mentioned by name in the Gospels, because they were well-known in early church times for their testimony to these crucial events in the origins of Christianity. It’s an accepted method of ancient historiography: the appeal to witnesses, many of whom could be cross-examined. It would have been hard to write, if there were not real people around to back up these claims.
Now both Graeco-Roman and Jewish sources from around the Mediterranean at this time indicated that a woman’s testimony was mostly considered unreliable at law. Much as it sounds sexist to modern ears, with the prejudice of those days, women were seen as gullible. So if you were embellishing a ‘Jesus story’ later on, you wouldn’t compound the difficulty by inventing women as key witnesses!
So the obvious reason for naming women is that the embarrassing fact was true. This is the criterion of embarrassment. Ironically, the reason for the report’s lack of credibility in the 1st century is the reason for its credibility in the 21st century!
Non-Christian sources
In regards to non-Christian sources, I mention Josephus (Antiquities 18:3, writing c. 93 AD, citing Jesus’ name, the method of crucifixion, and the governor who ordered it, Pilate), Tacitus (Annals 15:44, writing c. 115 AD, mentioning execution under Pilate, but not the method), and a bit later, Lucian (b. c.125 AD in The Death of Peregrine). I could add many others later, all of which pre-date the Qu’ran by a several centuries.
In regards to reliability of Josephus, and his so-called ‘Testimonium Flavianum’, there is enormous literature debating this issue. There are three main positions. The first, a minority position among scholars, favours its entire authenticity. The second, also a minority position, treats the entire section as Christian interpolation. The third, which is by far and away the majority position among scholars suggests Josephus mentions Jesus in this text but his words were subsequently doctored. While there is debate about how much of the material is interpolation, most include the reference to Jesus’ crucifixion under Pilate, while excluding part or all reference to the resurrection.
By contrast, it is an interesting exercise to ask sceptics for any extent examples of ancient non-Christian sources to the contrary, dating in the first or second century, and insisting that Jesus did not die by Roman execution, for example, suggesting that it only looked like Jesus was crucified!
Early dating
These reports, especially those in the New Testament, are early. Paul mentions the death of Jesus no later than 55 AD in 1 Corinthians and earlier in Galatians. And he reports he preached the same message to the Corinthians when he was with them in 50-51 AD, which is within 17-21 years of the time Jesus is said to have died (depending on whether you go for 30 or 33 AD). And the oral tradition formula he reports preaching in 1 Cor 15:3ff is widely assessed by scholars who have considered the subject to have been composed very early, reflecting what was taught by the Jerusalem apostles, very likely within a few years, or maybe even months of the events being reported.
For example, atheist scholar Gerd Ludemann, in The Resurrection of Christ: A Historical Inquiry (2004), agrees that,
the discovery of pre-Pauline confessional formulations is one of the great achievements of recent New Testament scholarship. (p. 37)
Indeed Ludemann thinks the formula within 1 Corinthians 15:3ff was composed very early, within,
the first two years after the crucifixion of Jesus. (p. 31)
All this underlines my point about the earliness of the reports of the death of Jesus. This is the criterion of antiquity.
By contrast, the Qu’ran dates no earlier than 610 A.D. when Muslims indicate that the angel Gabriel first appeared and began to speak to Muhammad. And so its testimony that Jesus did not really die on the cross dates more than 5 centuries later than the earliest written claims of his crucifixion. There is a massive gap back to the events it claims to report.
The verdict of modern historians
Historians judge on how they assess the balance of probabilities. Almost all scholars who have studied the subject conclude Jesus died by crucifixion. Here are some representative samples.
John McIntyre, “The Uses of History in Theology”, Studies in World Christianity 7.1, 2001:
Even those scholars and critics who have been moved to depart from almost everything else within the historical content of Christ’s presence on earth have found it impossible to think away the factuality of the death of Christ. (p. 8)
Gerd Ludemann, The Resurrection of Christ: A Historical Inquiry, 2004:
Jesus’ death as a consequence of crucifixion is indisputable. (p. 50)
JD Crossan, who denies the authenticity of many of the saying and deeds attributed to Jesus in the canonical Gospels, says in The Historical Jesus: The Life of a Mediterranean Jewish Peasant, 1999:
[there is not the] slightest doubt about the fact of Jesus’ crucifixion under Pontius Pilate. (p. 375)
He’s repeating his point from Jesus: A Revolutionary Biography, 1994:
That he was crucified is as sure as anything historical can ever be. (p. 145)
Geza Vermes, the late Jewish New Testament scholar, The Passion: The True Story of an Event that Changed Human History, 2006:
The passion of Jesus is part of history. (p. 9)
Bart Erhrman, renowned textual critic, but no friend of traditional Christianity, in The Historical Jesus: Lecture Transcript and Course Guidebook, 2000, says:
One of the most certain facts of history is that Jesus was crucified on orders of the Roman prefect of Judea, Pontius Pilate. (p. 162)
Roman Catholic scholar, RE Brown, The Death of the Messiah, 1994:
Most scholars accept the uniform testimony of the Gospels that Jesus died during the Judean prefecture of Pontius Pilate. (p. 1373)
It’s getting a bit tedious. I could cite many other scholars to this end.
Conclusion
I have used several standard aspects of reputable historical method (e.g. the criteria of multiple attestation, of embarrassment, of antiquity).
And the assessment that Jesus’ death by crucifixion is factual is shared by a very wide consensus of scholarship, including many of those unsympathetic to biblical Christianity. In fact, the wideness of the consensus is almost unprecedented in biblical scholarship.
I think it fair to say this manages the bias of my own horizons more than adequately. I am not so sure about others who ignore this consensus.
And so I am confident to say the Bible is absolutely correct and truthful when it says Jesus died by crucifixion and therefore (although I am sorry to put it so bluntly) the Qu’ran is wrong when it asserts Jesus did not die this way.