Is banjo threeie on GameCube a proper game?

Banjo-Kazooie is the first game and it is for the Nintendo 64, however there is now a port of the game available on the Xbox 360 (downloadable for a small fee from the Xbox Live Arcade).

Banjo-Tooie is the second game of the series and, as before, it is for the N64 with an XBLA port.

The third game of the series is called 'Banjo-Kazooie: Nuts & Bolts'. It is a very different experience / idea from the first two games and some fans of the game for this reason do not like it. It is for the Xbox 360 and you can buy it from some stores, although your best bet is online. It isn't perfect and you may be disappointed. Personally, I like the game a lot, but it took me a long time to accept where the Banjo series went.

The reason you may have the impression that the third game was for the Gamecube is because it was originally intended to be quite a few years ago. They did bring out a small tech demo, although I believe it was more of a trial of the Gamecube's features. That was going to be a more true sequel, as far as we know, but the idea was scrapped and Rare returned to it later after they moved to Microsoft.

I hope this supplies relevant information and helps you.