Jason from Priory School, Dunstable says:

"If you cut 2 squares deep it will become a 6 x 6 base which I make as the biggest amount of space: 72 cubes. I worked this out using :

Length x Width x Height
6 x 6 x 2 = 72"

Christina (Marborough Primary, London) and Josh (Ampthill, Bedfordshire) agree with this answer.

Josh said, "At first I thought it would be best to cut out a 3x3 square at each corner, but that box only held 48 cubes. If you cut out a 2x2 square though, the box will hold 2x6x6 cubes which is 72. That is the most."