Well, since nothing is mentioned in their description about remaining as an impediment to movement after they're dead I think it's reasonable to assume that they must in some way collapse, liquify, or evaporate at least to a point where they aren't any more of an impediment than any other very large corpse in a hallway. But where's the fun in that?
I like the idea that although they DO stop moving once their thicker, outer membrane is sufficiently damaged that the interior substance is less like jello and more like a thick liquid - the cottage cheese analagy is good. So their insides will leak out when cut up - but it takes a fair amount of cutting up simply by virtue of being 1000 cubic feet of critter, and that goo gets EVERYWHERE.
Don't forget that while it's alive a cube has to "swallow" stuff like coins and metal weapons and doesn't excrete or digest things like skeletons. It's a dungeon-cleaning monster after all. And those things don't sink to the bottom - they "float". That suggests that they don't just have watery insides.