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I lean towards Paul, but Oldhermit gave a very good argument for Apollos in his Hebrews Study thread. As Lynn stated earlier, all that really matters is that we pay attention to the words of the book.
Hebrews chapter 10 verse 34
For ye had compassion of me in my bonds, and took joyfully the spoiling of your goods, knowing in yourselves that ye have in heaven a better and an enduring substance.
Is there any mention in scripture that Apollos was ever in bonds? Off the top of my head, I certainly can't recall any. Also, whoever wrote this epistle was in Italy:
Hebrews chapter 13 verses 23 and 24
Know ye that our brother Timothy is set at liberty; with whom, if he come shortly, I will see you.
Salute all them that have the rule over you, and all the saints. They of Italy salute you.
Does scripture mention anywhere that Apollos was ever in Italy? I recall him being in Corinth and Ephesus, but I don't recall any mention of him ever having been in Italy, do you? We know that Paul was imprisoned and also in Italy and these are but two of many reasons why I lean heavily towards him being the author of the epistle to the Hebrews.