Consider the bottom plane of the 7x7x7 cube. The four corners of the 4x4x4 cube are at (0,0), (0,4), (4,4) and (4,0). The corners of two 3x3x3 cubes are at (4,0), (4,3), (7,3), (7,0) and (0,4), (0,7), (3,7), (3,4) respectively. The corners of three 2x2x2 cubes are at (3,5), (3,7), (5,7), (5,5) and (5,5), (5,7), (7,7), (7,5) and (5,3), (5,5), (7,5), (7,3) respectively. The remaining three 3x3x3 cubes are stacked on top of the 4x4x4 cube and 3x3x3 cubes. The remaining six 2x2x2 cubes are stacked on top of the three 2x2x2 cubes.
Hence, one 4x4x4 cubes = 64 units. Five 3x3x3 cubes = 135 units. Nine 2x2x2 cubes = 72 units. The remaining are 72 units of 1x1x1 cubes. Total 87 cubes make up 343 units. |