The GameSphere is a 6th generation game console, a parody of the Nintendo Gamecube. Its controller is an original Xbox controller, and the system itself is a Memorex Boomball.
Josh received the game console from his Grammy seen in "The Bet".
He and Drake were in a bet seen in "The Bet", to see how long he can stop from playing video games while Drake had to stop from eating junk food or who ever lose the bet must dye their hair pink.
In The Bet, it is revealed that the GameSphere has an accessory called "The Wireless Battle Pad" which is a wireless N64 controller.