There are 27 'peculiar cubes'. They're of the 'peg & hole' type, but for a clearer display, the holes have been replaced by red sockets.
Not surprisingly the puzzle is to pack the set into a 3x3x3 cube.
The two solutions are both of the most difficult type: with the blank cube in the center. For clarity the front- middle- and back-sections of the solutions have been colored differently.
Leaving out the blank and the 'ones', the remaining 24 cubes allow 2x3x4 solutions. Using only the 20 'threes', a 2x2x5 block can be solved. Note that in this case the flat cubes must occupy the middle and the hooked the corners. One solution of each type is displayed.
Peculiar Cubes © MindSports.