Do we have a record of Paul outside of the Bible?

The biblical record of the apostle Paul ends like this, just as Luke wrote it at the end of the book of Acts: For two whole years Paul stayed there in his own rented house and welcomed all who came to see him. Boldly and without hindrance he preached the kingdom of God and taught about the Lord Jesus Christ—Acts 28:30-31. There is admittedly not a lot of historical data concerning the apostle Paul beyond those final verses of the New Testament account, but the third century church historian Eusebius does give us some information. According to him, Paul was executed by beheading during the reign of the Roman emperor Nero, sometime between 65 and 68 AD. Because of his status as a Roman citizen, he was spared the prolonged agony of crucifixion (something his fellow apostle Peter is reported to have endured). Paul had been made a prisoner of Rome as a result of his arrest in Jerusalem and then had been shipped to the imperial city—Luke records this “fourth” missionary journey in the book of Acts chapters 27-28. Beyond that biblical account, it seems likely according to scholars that Paul was at some point released; following this, it is thought that he traveled to Crete. He mentions leaving Titus there in his letter to that pastor and protégé: The reason I left you in Crete was that you might straighten out what was left unfinished and appoint elders in every town, as I directed you—Paul, Titus 1:5. It is thought that, following his time there, he might have traveled west, possibly as far as Spain; he mentioned his plans to minister in Spain twice toward the end of his letter to the church at Rome (Romans 15:24, 28). Eventually he was arrested and imprisoned once again and brought back to Rome. This time, he would be martyred. As Eusebius tells it, “After defending himself, the Apostle was again set on the ministry of preaching . . . coming a second time to the same city [Paul] suffered martyrdom under Nero. During this imprisonment he wrote the second epistle to Timothy.” Paul ended that final letter with an unmistakable note of triumph: For I am already being poured out like a drink offering, and the time has come for my departure. I have fought the good fight, I have finished the race, I have kept the faith. Now there is in store for me the crown of righteousness, which the Lord, the righteous Judge, will award to me on that day—and not only to me, but also to all who have longed for his appearing—Paul, II Timothy 4:6-8. As a result of suspecting that his time left was short, he mentioned to Timothy, Do your best to come to me quickly—Paul, II Timothy 4:9. But despite that concern, he ended his final letter to Timothy with these words: The Lord will rescue me from every evil attack and will bring me safely to his heavenly kingdom. To him be glory for ever and ever. Amen—Paul, II Timothy 4:18.
In addition to Eusebius, we have early historical attestation of Paul’s work alongside Peter in Rome through the writings of Ignatius of Antioch (35-110 AD), a first-century disciple of the original apostles. Ignatius supports Paul’s credentials as an apostle. He fully endorses the gospel message that Paul preached to the Ephesian church, and he seconds Eusebius’ report of Paul’s martyrdom. In a letter of his to Polycarp, a disciple of the apostle John, Ignatius makes several references to Paul’s writings, regularly quoting from him. Ignatius himself also died a martyr’s death, being fed to the lions in a Roman coliseum.
We also have Clement, a first-century Christian who as secretary to the church in Rome was reportedly in charge of correspondence with other churches. A second-century church leader, Irenaeus, wrote the following about Clement: “. . . after him, in the third place from the apostles, Clement was allotted the bishopric. This man, as he had seen the blessed apostles, and had been conversant with them, might be said to have the preaching of the apostles still echoing [in his ears], and their traditions before his eyes. Nor was he alone [in this], for there were many still remaining who had received instructions from the apostles.” Clement himself, writing in 96 AD, said this about the apostle Paul: “Owing to envy, Paul also obtained the reward of patient endurance, after being seven times thrown into captivity, compelled to flee, and stoned. After preaching both in the east and west, he gained the illustrious reputation due to his faith, having taught righteousness to the whole world, and come to the extreme limit of the west, and suffered martyrdom under the prefects. Thus was he removed from the world, and went into the holy place, having proved himself a striking example of patience.”
Finally, we have the writings of Polycarp of Smyrna (69-155 AD), mentioned previously as a disciple of the apostle John. He himself wrote about Paul: “For neither I, nor any other such one, can come up to the wisdom of the blessed and glorified Paul. He, when among you, accurately and steadfastly taught the word of truth in the presence of those who were then alive. And when absent from you, he wrote you a letter, which, if you carefully study, you will find to be the means of building you up in that faith which has been given you, and which, being followed by hope, and preceded by love towards God, and Christ, and our neighbour, is the mother of us all. I exhort you all, therefore, to yield obedience to the of righteousness, and to exercise all patience, such as you have seen [set] before your eyes, not only in the case of the blessed Ignatius, and Zosimus, and Rufus, but also in others among yourselves, and in Paul himself, and the rest of the apostles.” His contemporary Irenaeus noted of Polycarp that he was a Pupil of John and a Pupil of the Apostles being appointed Bishop of the church in Smyrna by the Apostles themselves. Irenaeus also writes of Polycarp: “For, while I was yet a boy, I saw you in Lower Asia with Polycarp, distinguishing yourself in the royal court, and endeavouring to gain his approbation. For I have a more vivid recollection of what occurred at that time than of recent events (inasmuch as the experiences of childhood, keeping pace with the growth of the soul, become incorporated with it); so that I can even describe the place where the blessed Polycarp used to sit and discourse— his going out, too, and his coming in— his general mode of life and personal appearance, together with the discourses which he delivered to the people; also how he would speak of his familiar intercourse with John, and with the rest of those who had seen the Lord; and how he would call their words to remembrance. Whatsoever things he had heard from them respecting the Lord, both with regard to His miracles and his teaching, Polycarp having thus received [information] from the eyewitnesses of the Word of life, would recount them all in harmony with the Scriptures. . . . inasmuch as these things had been always [so] observed by John the disciple of our Lord, and by other apostles with whom he had been conversant . . . But Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true.” So YES, there is substantial extra-biblical support for the life, work and words of the apostle Paul.