Nintendo does not make a profit on the GameCube systems.
In fact, all console manufacturers will take a $50-$250 loss per console, in an effort to create a large user base. This allows them to sell games for $50 that cost them maybe $10 per copy once you figure out the production stuff. The markup in the games is where they make their money, and it more then makes up for the initial losses of any console.
This is why Sega has pulled out of the hardware sector and is sticking to producing games for other peoples systems. They've lost too much on Saturn and Dreamcast, so they cater to the userbase of other systems which is already there. Mind you the goal for any manufactuer is to have games exclusive to their system in an effort to increase the user base further.