Totally depends on the game. Not all games are even sequenced to begin with, so there may not be any separate data for instruments/sequences/whatever, and in that case you're simply out of luck.
A lot of GameCube games (though certainly not all) use an audio framework called MusyX, however, for which there are some tools available.
You can use amuse to play MusyX files (.sdir, .samp, .proj, .pool, .song). If you're lucky, the files will be readily extractable from the GameCube filesystem, but otherwise you'll obviously need appropriate tools to extract data from the game you're dealing with.
If you want to extract samples, I wrote a script to do so: musyx-extract
Also, soneek has written a MIDI converter called musyx2midi, but I don't know if he ever "finished" it or uploaded it anywhere publicly.
Did any GameCube games use the MORT speech audio compression? Or was that only N64 games. Since I reversed that, I was wondering if any GameCube happened to use it.