How about a cube case for a mini-itx mboard. Haven't got one myself, but it's about the size you mention. I went with the super-slim ITX case that's even smaller (not really any room for a PCI card)
The boards are about $98 US, the guys I linked to above for the case also sell the motherboard. Another source for those boards and cases is www.caseoutlet.com, but haven't purchased anything from them myself.