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The Bible says nothing about Paul’s actual death.
The last we hear is in the second letter to Timothy written by Paul during his final period of captivity in Rome.
2 Timothy 4:6 For I am already being poured out as a drink offering, and the time of my departure is at hand. 7 I have fought the good fight, I have finished the race, I have kept the faith. 8 Finally, there is laid up for me the crown of righteousness, which the Lord, the righteous Judge, will give to me on that Day, and not to me only but also to all who have loved His appearing.
I hope this helps.