Someone else said that, but yes you do need 3 conductor + ground.When you said "You will need 4 wires available" I thought you were referring to the stove outlet. Not sure if current stove breaker is GFCI because I'm not there. Most likely its not.
I would need something like this ...
You're on the right track with that breaker, you need a disconnect within sight as well.
I'm in Canada, so I'll let the NEC guys chime in. But an 8kw would need #6 on a 50A gfci up here.
*edit* actually we could get away with #8, but CEC has different ampacity charts than NEC