Is Sonic Adventure on GameCube?

No. Sonic Adventure (1998) launched on Sega Dreamcast.

Sonic Adventure DX: Director's Cut (2003) was ported to GameCube (and PC). It includes:

• Updated textures/models (mixed reception).
• Mission Mode (60 missions).
• Game Gear games unlockable.
• Chao Garden connectivity via GBA link cable.

For the original Dreamcast experience, play via Flycast (emulator) or Dreamcast hardware. SADX on GC/PC is the official way on Nintendo hardware.