Gamecube games cannot be backed up in the sense that you take an original, copy it's data, burn it onto a mini-dvd and then it will play in your machine...
The only current method to allow you to play games is:
You need to buy a broadband adapter
You need to buy fantasy star online
Cat5 crossover cable
Then what you need to do is connect the gamecube to your pc via the crossover cable and the bb adapter.
Then run fanstay star online and set up the network in it's services.
From here you swap the disc and ftp the files from the gamecube to your pc (just like xbox)
Now you cannot burn these files straight onto a minidvd, same way it cannot be done on xbox and ps2. What you need to do is stream the files back to your gamecube and play the game as though your pc was the disc. This way it plays but unfortunately with data rate the games play exceddingly choppy and all in all it's not a very nice experience.
The best thing to do is buy an xbox........