Copy XBox360 games to central server

I’m looking for a way to copy (legally, of course) my XBox360 games to a central server.
The reason for this is: I have several XBox360’s in my house. They’re used mainly as media center extenders but, sometimes the kids want to play games on the ones in their rooms. It would be nice to have our games stored on a central server so that the physical game CD’s don’t have to travel around the house (and get lost in the kid’s rooms).
I’ve got a gigabit network, so network speed shouldn’t be an issue.
Is this setup possible?

Legally impossible, since a non-modified Xbox 360 cannot execute any untrusted source.