We have been very happy with the cubes we have made. We make them out of solid styrofoam, usually 2" blue but we have made some out of bead foam also that you can get for drop in ceilings. Our usual size is 18x18x24 and we cut the foam on the table saw to 24x18 and layer it 18 high. Then we cut lauan sides 18X18 and 18X24 (we don't include the overlap as the short sides serve to radius the corners. The whole kit and kaboodle is held together with gaffers tape taping the edges together. Then the whole cube is covered in muslin and glue. These cubes are lightweight, light enough that they can be tossed between people. They are durable, stackable, take plenty of weight. And also conform well to the
typical method of rehearsal cube movement (i.e. being kicked from one place to another) without marring the floor surface, even the dance floor. Our oldest cubes are perhaps 8 years old now and we have yet to even recover them, although they have been painted many many times.
I've adapted them, but what I do is use sheet foam, cut and stacked to form a cube. Cover with 1/4" ply (not Luan, real Plywood.) Tack the edges with an air stapler to hold the thing together long enough to gaff tape out the edges. Cover that with muslin, size and paint.
The actor-folk like them because they are nice and lightweight. I like them because they are nigh invulnerable. They're very popular, as they are extremely light, but stable. For this place, I built several each 24x24, 24x30 (or 36...barstool height), and a large bar-sized one. They hold up reasonably well with the only maintenance being re-taping and repainting.
We made a whole collection of elements that were based on a 16" module that allowed most efficient use of sheet goods. There were many actual cubes (16x16x16) as well as some double and triple wides (16x16x32/48). There were pieces that looked like a plain straight back chair on the same module with the back about 4" deep. There were just a couple of double and triple wides in this style. Used 3/8 AC ply. All edges were mitered and joinery was by use of 54/x5/4 nailer cleats inside each edge. Much glue and then slightly chamfered when complete. We incorporated slots for hand holds in all units as well.