Mac OS X 10.5 requires an 867MHz CPU to install off the DVD, but you could pull the hard drive, install it using another machine, then put the HD back in the Cube. There is a way to hack the installer, but you'll have to do a Google search for that.
Leopard will run, but you wont be happy.
10.4.11 is the best OS for a Cube, IMHO. I have it installed on my Cube - with a 1.7GHz PPC7447 (1MB L2), GeForce 6200 video card, a 120GB HD and 1GB of RAM. Runs well for basic web, email, office apps, etc., but things like Flash video will really show the age of the Cube as it'll get hung up on the measly 100MHz bus.