The GameCube (also can be abbreviated to GCN) is a system created by Nintendo. It was released in 2001 along with the Game Boy Advance. The only Mario Kart game released for it was Mario Kart: Double Dash!!, which was released in 2003. Like it's predecessor, the Nintendo 64, it also had revolutionary graphics and has four controller ports.
The GameCube uses the abbreviation GCN because NGC was already used as the abbreviation for the Neo Geo Pocket Color, a handheld console made by the SNK Playmore Corporation two years earlier. This strange abbreviation would become especially noticed in Mario Kart DS and all the Mario Kart games to follow, due to how retro courses from Mario Kart: Double Dash!! would use this name, while courses from other games used standard abbreviations from their respective consoles (i.e. SNES, N64, GBA, DS, Wii, 3DS)