Erick (Sciennes Primary School, Edinburgh) sent in this solution:
Here is how you do it. The top level is first, then the middle, then the bottom:
This collection of solutions from Moorfield Junior School shows how the layers can be placed in different orders, or the whole cube turned upside-down, or described from different angles.

Kelly and Josephine showed their solution in another, rather clever way. They used letters, but we have used coloured squares to help you see how this net would show all the little cubes when it was folded into a cube.