My suggestion would be to look around Wal Mart, Linens and Things, and any other place that carries nic nac foo foo crap. You are bound to find a glass or acrylic cube somewhere that is used for some other reason. Then just make sure it is water-tight or can be made so. A bead of aquarium safe silicone would do wonders as long as there are no substantial gaps in the seams.
That is about the only way to find one for under $20. Of course you would have to build a hood and add your own filter. But if you are stuck on the cube aquarium idea it could be done relatively cheaply.
Disclaimer: Any errors in spelling, tact, or fact are transmission errors.