Well, if you're looking for a fairly ideal server case for mini-itx, you'll probably want to take a look at this one:
The chenbro ES34069 Mini-ITX Home Server/NAS Chassis has 4 hot swap 3.5" sata hard drive bays, and space for a slim optical and a 2.5" laptop drive as well. Not sure how quiet it is, though. If you really have to have it more cubical, you might go with:
The Venus 668b is roughly the size of the standard shuttle box, with two 5.25 bays and 2 3.5 bays. Hopefully it won't be as noisy as the average shuttle box. The Lian-Li case you mentioned is actually a micro-atx cube style case, and I recently heard about this one:
Which claims to have 2 external 5.25 bays, 1 external 3.5 bay, and 4 internal 3.5 bays. But it's even bigger than the average micro-atx case, although smaller than a standard atx. With the extra size though, it might be easier to keep cool, and thus be quieter. Hard to say, though.