Bob:
I don't fully understand your question.
Is the spa 240 volt, 3 wire (hot/hot/neut/grd) or 2 wire (hot/hot/grd)??
How does the 120 volt GFi "fit-in"?? If you "tap it off" of the 50 amp feeder, how are you protecting it?? (OCP)
The prime answer is "yes" you can protect 8 THHN Cu at 50 amps per NEC 310-16, before you do any de-rating, if required.
The above is my humble opinion.
John