Find a dissection of a 19x19x19 cube such that all the pieces are cubes with integer dimension and none of them are unit cubes.
(In reply to
re: first observations by Jer)
Please refer to George Sicherman's dissection of a 19 cube just using 3,4,5 and 7 cubes.
http://www2.stetson.edu/~efriedma/mathmagic/0714.html