Can I use a three wire cable to feed a whirlpool tub?
As long as the circuits are 120V you can run a 3-waire cable. The only caveat is that you would then need to use a two-pole GFI breaker to protect the circuits.

With two 2-wire circuits and single-pole GFI breaker (or devices) you can isolate the circuit for troubleshooting and maintenance.