Which was written first, the Epistles of Paul or the Gospels?

The epistles of paul. Corinthians is probably the earliest part of the new testament, it was written in the late 50's AD. The earliest date usually given for the gospels is around 60AD.

The earliest that the gospels can be dated to is 70AD this is the Gospel of Mark, at least some of the Epistles can be dated earlier to 50 AD

First, there really is no "academic consensus" as to the dates of any NT books. Honest bible historians (and there are damn few of them) give a wide range of possible dates; dishonest ones claim to "know" with more certainty. See, not even the authors are known, let alone any dates for their original writing. The date ranges have to be inferred, with great uncertainty, largely from *other* works we DO have dates for, that quote NT books ("this had to have been written by this date, since it's quoted directly in this other work for which we do have a date").

So while *most* (but not all, by any means) bible scholars put the epistles of Paul before all of the "gospels" except possibly (but not with any certainty) "Mark," that's largely guesswork.