Embellishments in the Gospel of Mark.

[Fake Messiah]

we know luke's work where complete by then as he was apart of Pauls efforts as paul mentions luke several times

Problem with that argument is that Paul mostly mentions Luke in Deutero-Paulines and Pseudo-Paulines, meaning not written by Paul but forgeries - so there is no point talking about them.

Now, Paul does mention certain Luke in one of, what is considered, his works and that is Epistle to Philemon 1:23–24, but it only says that some Luke along with Epaphras, Mark, Aristarchus, and Demas, is said to be sending his greetings to Philemon, there is no reason to put much trust of who that Luke was. Not to mention that nowhere in Acts or Luke does the author claim to be a companion of Paul and if that Luke was with Paul and Paul's student he probably wouldn't disagree with Paul's theology, either.