The title nearly says it all: what is the fewest number of cubes that can be fused face-to-face into a polyhedron that does *not* fill space? The smallest that seemed like a sure non-tiler to me was 9: seven in a ring missing one "corner", plus one above one of the "middle" cubes of this ring, and a final one fused to that one, positioned above the hole in the ring. Then there seemed to be no way fill the hole in the ring with another copy of this polycube -- but **EDIT:** as Georgios points out in a comment to his answer, you can actually interlock a pair of these to get a simply-connected compound. So the smallest *truly* obvious non-filler is a decacube, consisting of an 8-ring with two attached to a middle cube to "cap" the hole.

But I wouldn't be surprised if there were an octacube or heptacube non-space-filler, and if so, I suspect it's well-known to some folks. However, I can't seem to find a reference, even though the answer to the corresponding question for polyominoes in 2D is easy to find, e.g. [MathWorld](https://mathworld.wolfram.com/PolyominoTiling.html) notes that all but four heptominoes tile the plane, as all smaller polyominoes do.