A cube is painted, and cut, something like this.
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LOGIC
•For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1,
•Number of cubes with 0 side painted= (n-2) ^3
•Number of cubes with 1 sides painted =6(n - 2) ^2
•Number of cubes with 2 sides painted= 12(n-2)
•Number of cubes with 3 sidess painted= 8(always)
•For a cuboid of dimension a*b*c painted on all sides which is cut into smaller cubes of dimension 1*1*1,
•Number of cubes with 0 side painted= (a-2) (b-2) (c-2)
•Number of cubes with 1 sides painted =2[(a-2) (b-2) + (b-2)(c-2) + (a-2)(c-2) ]
•Number of cubes with 2 sides painted= 4(a+b+c -6)
•Number of cubes with 3 sidess painted= 8
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