Someone has never listened about the Gamecube Controller Adapter for Wii U and Switch.Sadly no, you cannot use an actual Gamecube controller with the Wii U, as it does not have the controller ports the original Wii has.
You can use an Injector to play Gamecube games with the Wii U Gamepad or if you have a classic controller for the Original Wii then you can use that for Gamecube games.