The Wii U has the ability to play GameCube games via a Wii OS emulator. The Nintendo Wii was able to play Gamecube games as it had a hardware input that let you connect a GameCube controller and memory card directly into the system.
The Wii U does not have any hardware connection built into the machine that will allow you to use GameCube controllers. It is still possible to use a Gamecube controller with the Wii U though.
The Wii U has 2 USB ports that can be used to expand the systems functionality. If you look online it is possible to buy a USB addon, both official an unofficial that will allow you to connect your GameCube controllers directly to the Wii U system, via USB and the controllers will work perfectly for your video games.