Running a GameCube (23 watts) literally nonstop for a year would use a little over 200 kWh.
Assuming average USA electricity prices, in 2002 electricity cost ~$0.09 per kWh, so one year of that would cost an additional $18.00. That number only tends worse going forward.
A GameCube memory card would cost about $11.
As usual, it's more expensive to be poor.