Can you play a Virtual Console GameCube game with a classic controller?

yes you can use a classic controller or you can use a gamecube controller...also u need a gamecube memory card to save. Its in the wii manual.

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Correction No you cannot.
The GameCube feature disables the Wii side of the console, so the wii-motes won't work or the attached "classic" controller.
You have to have a GameCube Controller that plugs into the GameCube controller port