Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Can you work out the dimensions of the three cubes?
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
Take a look at Painted Cube to think about how to visualise parts of a cube.