Is Soulcalibur III on GameCube?

Yes. Soulcalibur III was released on GameCube in 2005 (NA: Oct 25, JP: Nov 17, EU: Nov 18).

It is the only mainline Soulcalibur on GameCube. Soulcalibur II (2003) featured Link as a GC-exclusive guest character; SC III had no platform-exclusive guests.

Note: The GameCube version lacks the Chronicles of the Sword strategy mode (PS2 exclusive) and has fewer Create-a-Soul parts.