The first thing I would do is verify the size of the cable supplying the sub panel. It wouldn't be unheard of to use a 30 amp cable with a panel that's rated higher.
It should be a #6 cable to run a 50 amp, so if that's the case you could run the tub, but theoretically that would be all. Normally a person would run more than needed, which in your case would be better if it was a #2 or 100 amp cable.
Considering the downside, which could be an electrical fire, I would run a separate cable for it. Those tub heaters can pull some amps in the winter time.
Maybe you'll get lucky and the cable was oversized.
