The 8GB needs to be installed on Your Console's Hard Drive. The Xbox Cloud is a server that can hold your saved games on the internet. It is not meant to hold DLC or full games.
The cloud only has about 1/2 of a GB on it.
Grand Theft Auto 5 has a mandatory install you probably should go get a hard drive for your Xbox 360 or if you can't afford one go get a USB flash drive with at least 10GB labeled storage as the formatting will take up some of the room.