This little animation shows how formations of basic shapes can produce other larger shapes.

The Checkerboard – 1x8x8
Notice how two 1x4x4's also form the 1x4x8 and then the 2x4x4.
Two 1x4x8's also form the checkerboard, the 1x4x16, and the 2x4x8.
An animation of the 1x8x8 checkerboard may be viewed at This page.
An animation of the 4x4x4 cube may be viewed at This page.

The Challenger -1 x6x6 (only 1 solution)
Solved by Abel Garcia
The 'H' piece does not work in a 1x6x6 grid

The Super Challenger – 2x5x6 (only 1 solution)
Solved by Dave Hecker
As with most shapes, you can calculate the piece NOT to use. Since the total cubes for this shape is 60 and only 2 pieces have 4 cubes each, simple logic allows the removal of one piece since dark and light colors must be equal.

For more details and hints for solving various shapes see the SOLUTIONS! pages.