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The answer depends on how many 1 cm cubes you start off with. If you had n cubes then the largest hollow cube is a k-cube where k^3 <= 6n^2 - 12n + 8

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Q: Largest hollow cube you could get from 1 cm cubes?
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A 10cm X 10cm X 10cm cube is cut into 1cm X 1cm X 1cm cubes some of these cubes are put together to form the largest possible cube looks solid on the outside but is hollow how many cubes are left?

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