Styro or wood?
Corvus, you haven\'t said what you are making the base out of. Styro shouldn\'t be a problem to carve the square out of, so i am assuming wood or similar.
Make the base in layers. The top layer equal in thickness to the base thickness. Cut holes where you want the bases to be then finish the holes with a saw: Sabre, Jig, Coping.
The coping saw will be the most cost effective way to go if you don\'t own the other power tools.
release the saw blade, poke it through the hole, re-attach it to the saw and cut away.
If you want to make it from one piece of wood, you are looking for for a forestner bit (think expensive) or router bit or dremil bits.
followed up with a set of good chisels to make the corners square, or fine dremil tools to make the corners almost square.