All these methods assume you have modded your vWii. If you have not, follow this guide here.
The Wii U can natively run GameCube games due to its hardware backwards compatibility with the Wii, however the Wii U is unable to read GameCube discs. There are still multiple ways to run GameCube Games, but a modded Wii (or GameCube) is required to dump the discs.
Dumping GameCube games:
To dump GameCube games from a modded Wii follow this guide here.
Method I: Nintendont
Nintendont allows you to load backups of your GameCube games natively on (v)Wii from an external drive connected via your Wii U's USB ports, or SD card.
Pros: does not require a Wii Virtual Console title, can be loaded from an SD card.
Cons: can't be loaded from the Wii U Main Menu, can't be stored on a Wii U formatted drive.
Instructions
The process for setting up Nintendont on vWii is identical to that of the Wii's. Please follow the Wiki Hacks Guide page linked below.
UWUVCI allows you to inject any GameCube backup into a preexisting Wii Virtual Console title, package it with Nintendont, and install it to your Wii U's internal storage, or an external drive connected via the Wii U's USB ports.
Pros: can be loaded from the Wii U Main Menu, has GamePad support, can be stored on a Wii U formatted drive.
Cons: can't be loaded from the SD card, requires a Virtual Console title to have been purchased prior to the E-Shop closure.
