Measure the length of the edge of your cube and divide it into three unequal lengths. The longest is called A, the medium length is called B, and the shortest is called C. For example, if your cube is 9 inches cubed, you may choose to make A equal 4 inches, B equal 3 inches, and C equal 2 inches.
Place the cube in a clamp and carefully saw it into three slices with widths of A, B and C from left to right.
Turn the cube a quarter turn clockwise and replace it in the clamp. Carefully repeat the same cuts in a new dimension, cutting three slices of widths A, B and C straight through the cube. The result should be nine rods with varying dimensions.
Rotate the cube forward a quarter turn, bind the rods together in a cube shape with the rubber band, and repeat the same cuts in the third dimension, cutting straight through in three slices with widths A, B and C. The result should be 27 pieces of which three are cubes (with edges A, B and C, respectively) and the rest are rectangular prisms of various dimensions.
Sand the surfaces of the pieces and smooth the corners and edges.
Paint the blocks according to their sizes and shapes. Paint each square face red if its edges have a length of A, blue if length B, and yellow if length C. Paint each rectangular face black. The result should be one large red cube, one medium-sized blue cube, one small yellow cube, six rectangular prisms that are entirely black and 18 rectangular prisms with one colored face (six of each color).