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For the $2$ by $2$ cube
Green Cube, Yellow Cube
Age 7 to 11
Challenge Level 
For the $2$ by $2$ cube
Idil (Private IRMAK Primary & Secondary School, Istanbul, Turkey) says:
All of them must be the same. Three faces with one corner in
common will be yellow, the other three faces with the
diagonal corner will be green.
Jason (Priory School UK), Christina (Malborough Primary School, UK), and Dogan (Private IRMAK Primary & Secondary School, Istanbul, Turkey) drew a net of a cube to show the colour of each face.
For the $3$ by $3$ cube
Dogan Private IRMAK Primary & Secondary School, Istanbul, Turkey) explains that:
We can paint corners the same as we did before. Then we can paint cubes in the middle like two sides yellow, two sides green - you don't need to paint the other sides. The following figure shows an opened middle cube and how it should be painted:You may also like
Little Boxes
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?