One more time for the record
The Gamecube will not run on anything less than 10v on the 12v line using the Gamecubes Regulator.
The Gamecube and any other electronic device is more efficient at lower voltages. Meaning at lower voltages they will use less overall power. But they will draw more amperage.
So say a device draws 1A at 14.4v , it will probably draw around 1.1A at 12v. That would mean at 14.4v it uses 14.4 watts but at 12v it only uses 13.2 watts. But it draws more amps so you have to compensate with higher mAh batteries.