Can I play an xbox digitally downloaded game on a different console?

I downloaded minecraft on my xbox(no hard copy), and I'm going to my girlfriends tomorrow to play it, but we want to play the world we have in my saved games. As long as i download my profile over xbox live will i have my same world?

You don't actually have to have a flash drive like the other answer says. You just have to transfer the save game for the world to the cloud storage. Then, when you play Minecraft on the other console, the Xbox will sync. The cloud storage and you'll be able to play on the world from there.

You won't have your world as it is saved on your Xbox 360, but you can use a flashdrive, move your world and profile onto it, and then you can bring it with you and plug it into her Xbox 360 and play on your world that way.

Yes but you have to be online.