Designed by John Conway, copyright ThinkFun Binary Arts 2003.
(plastic, box and 9 pieces, 1.75" solved)
Also known as Conway's Curious Cube, and described on pages 736-737 of the Winning Ways books. Three unit cubes and six 1x2x2 pieces must be placed in a 3x3x3 box. In the unique solution, the three unit cubes line up diagionally through the cube from a corner to the center to the opposite corner:
Here is the solution that was sold with the puzzle: