The figure below resembles a staircase, so call it a staircase polyomino. (This instance is size 5)

X
XX
XXX
XXXX
XXXXX

Give a staircase polyomino unit thickness to form a solid. It is trivial to pack n of the size-n staircase polyominos into a nxnxn cube.

Prove or provide a counterexample to the statement: It is impossible to pack n+1 of the size-n polyominos into a nxnxn cube.