Cubes with 6 Colors
These are the famous 30 colored cubes known as MacMahon cubes. A 2x3x5 box can be made with the complete set.
Inside the box colors are matching and opposite faces of the whole box have same colors, too.
You may ask for a box where each face has a different color but this isn't possible because the 3x5
faces have an odd number of squares and the frequency of each color is even.
A solution showing the layers is provided if a solution by hand fails.