The GameCube failed because Sony was able to go unchallenged for nearly two years building up a strong user base and irreversable momentum. As many said DVD played a major role in building the PlayStation empire. Lets also remember that Nintendo64 failed to kill the PSOne, thus PS2 had momentum by default (Having lead the last generation)
But Nintendo didn't count GameCube as a failure. Nintendo still made millions upon millions of dollars off of software sales alone. I think as Rol said recently only once in the GameCube's life span did Nintendo actually have a loss and it was only like 30-million dollars barely anything opposed to Sony and Microsoft's expenditures.
In the end the GameCube was a success, it sold Nintendo's first party software and Nintendo has alway survived by selling software not hardware. Nintendo themselves at the launch of the Wii said they would be willing to handle 100% of the Wii's gaming, they didn't care if third parties would support the platform or not. That is just how strong Nintendo is, they make such good games that they will turn a profit with or without help from third parties!
-JC7
"In God We Trust - In Games We Play " - Joel Reimer
