Are there any non-biblical accounts of crucifixion?  Yes, there are.  Ancient texts clearly mention crucifixion, as does the Bible.  Please consider the following list.

1. Josephus  born in AD 37 was a Roman historian
   1. In antiquities 12, chapter 5, “But the best men, and those of the noblest souls, did not regard him, but did pay a greater respect to the customs of their country than concern as to the punishment which he threatened to the disobedient; on which account they every day underwent great miseries and bitter torments; for they were whipped with rods, and their bodies were torn to pieces, and were crucified, while they were still alive, and breathed.”
   2. Antiquities 17: Book 10, “Following the death of Herod in 4 B.C.E. there were outbreaks of revolt throughout Judea. Varus, the Roman legate of Syria took two legions and brutally pacified the country, particularly in Galilee., “Upon this, Varus sent a part of his army into the country, to seek out those that had been the authors of the revolt; and when they were discovered, he punished some of them that were most guilty, and some he dismissed: now the number of those that were crucified on this account were two thousand.”
2. Ignatius d. 117
   1. “Do not err, my brethren. Those that corrupt families shall not inherit the kingdom of God. If, then, those who do this as respects the flesh have suffered death, how much more shall this be the case with any one who corrupts by wicked doctrine the faith of God, for which Jesus Christ was crucified! Such an one becoming defiled in this way, shall go away into everlasting fire, and so shall every one that hearkens unto him.” – Ignatius (Epistle to the Ephesians, 16).
3. Justin Martyr   100 – 165
   1. First Apology, 61, “And in the name of Jesus Christ, who was crucified under Pontius Pilate, and in the name of the Holy Ghost, who through the prophets foretold all things about Jesus, he who is illuminated is washed.”
   2. “For there is not one single race of men, whether barbarians, or Greeks, or whatever they may be called, nomads, or vagrants, or herdsmen living in tents, among whom prayers and giving of thanks are not offered through the name of the crucified Jesus,” (Dialogue with Trypho, 117).
4. Tertullian 160 – 220
   1. By this Praxeas did a twofold service for the devil at Rome: he drove away prophecy, and he brought in heresy; he put to flight the Paraclete, and he crucified the Father.” (Against Praxeas, 1).
5. Origen 185 – 254
   1. “Origen insisted that, like all human beings, she [Mary] needed redemption from her sins; in particular, he interpreted Simeon’s prophecy (Luke 2, 35) that a sword would pierce her soul as confirming that she had been invaded with doubts when she saw her Son crucified.” (J.N.D. Kelly, Early Christian Doctrines [San Francisco, California: HarperCollins Publishers, 1978], p. 493).
6. Cyprian d. 258
   1. “And from the sixth hour to the ninth, the Lord, being crucified, washed away our sins by His blood; and that He might redeem and quicken us…” (On the Lord’s Prayer, 34-35).
7. John Chrysostom   347 – 407
   1. “For having recently acquired the empire of the world they were elated, and lived in riches and luxury, and fishermen brought the preaching there, and they Jews and of the Jews, a nation hated and had in abomination among all men; and they were bidden to worship the Crucified, Who was brought up in Judea.”
8. Ambrose 337 – 397
   1. “For He promises forgiveness to all who are converted, since it is written: ‘Whosoever shall call on the Name of the Lord shall be saved.’ And lastly, the Jewish people who said of the Lord Jesus, ‘He hath a devil,’ and ‘He casteth out devils through Beelzebub,’ and who crucified the Lord Jesus, are, by the preaching of Peter, called to baptism, that they may put away the guilt of so great a wickedness.” (Two Books Concerning Repentance, 2:4:24, 2:4:26).
9. Augustine  354 –  430
   1. “But He instructed them, and saith unto them, ‘It is the Spirit that quickeneth, but the flesh profiteth nothing; the words that I have spoken unto you, they are spirit, and they are life.’ Understand spiritually what I have said; ye are not to eat this body which ye see; nor to drink that blood which they who will crucify Me shall pour forth.” (Expositions on the Psalms, 99:8)
   2. “This seems to enjoin a crime or a vice; it is therefore a figure, enjoining that we should have a share in the sufferings of our Lord, and that we should retain a sweet and profitable memory of the fact that His flesh was wounded and crucified for us.” – Augustine (On Christian Doctrine, 3:16:24)
10. Cyril of Alexandria    376 – 444
    1. “He tries to imagine the thoughts that passed through Mary’s mind. Had Jesus been mistaken when he said he was the Son of Almighty God? Why was he crucified who said he was the life? Why did he who had brought Lazarus back to life not come down from the Cross?”