No. Tony Hawk's Project 8 (2006) was not released on Nintendo GameCube.
The GameCube received the previous two mainline entries:
By the time Project 8 launched, Nintendo had moved focus to the Wii (released Nov 2006). The Wii received Tony Hawk's Downhill Jam (2006) instead—a different, arcadey downhill racer.
If you want the "classic" THPS feel on Nintendo hardware, THUG 2 on GameCube (or Wii via backward compatibility) is the last mainline entry.