Thirty Colored Cubes puzzle

Thirty Colored Cubes puzzle is a game devised in 1921 by Percy MacMahon, which was marketed under the name 'Mayblox.' It is played with 30 cubes that have all possible permutations of six different colors on their faces. A number of different games can be played with the blocks. One is to choose a cube at random and then choose seven other cubes to make a 2 × 2 × 2 cube with the same arrangement of colors for its faces as the first chosen cube. Each face of the 2 × 2 × 2 cube has to be a single color and the interior faces have to match in color. After building one such cube, only one other with the same properties can by made from the remaining 22 cubes – the mirror image of the first.