Subpanel run to secondary floor apartment from basement
Just to answer the question..

You'd need 4 (Hot, Hot, Neutral, Ground) #1 AWG wires.


1 AWG supplies up to 110 amps
6 AWG supplies up to 55 amps


If you use the 6 AWG, you could only feed the subpanel with a 50A breaker. Essentially making it a 50A subpanel. It's best to go ahead and get the most out of it if you can by using #1 wire.