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If the statement that it contains 24 cubes requires that the sides are integer, then the minimum suface area is for a 2*3*4 cube, with a surface are of 2*(2*3 + 3*4 + 4*2) = 2*(6+12+8) = 2*26 = 52 square units.

If, however, you are not restricted to integer solutions, the minimum surface area is achieved when the sides are of length 24(1/3). Then the surface area is 6*24(2/3) = 49.922 square units.

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