the bigger the better. gotta watch the max amperage the inverters will put out. look at the AC cord for the game system, there will be an output rating there that will tell you how many amps the system draws.
Check the gamecube and see how many volts it will draw. Usually it will be a range because it will draw a surge current when you push the power button on it, and then the voltage requirement will drop once fully powered.
Take that voltage and multiply it by the amperes the gamecube draws. That will give you the watts.
You will need an inverter that can handle the initial surge. For example, for my xbox I have a 300W Continuous/600W Surge Peak Inverter. Maybe you should go for the same.
Also, what most people don't realise, is that you cannot plug this inverter drawing that much power into your cigarette lighter...
What you need to do:
1) Run a 35 amp fused 8-10 Gauge wire directly from the battery or power distribution block to the destination area of the inverter.
2) hook up that wire to the inverter. plug in your gamecube.
3) done
of course this is A HIGHLY SIMPLIFIED description, any questions ask me.
Just as a reference point... the xbox uses 150W peak, and ~100 or so continuous(i've chipped/softmodded around 80 boxes). But like brandon said, more is always better.