A large solid cube is assembled by gluing together idenical

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A large solid cube is assembled by gluing together idenical unpainted small cubic blocks .All six faces of the cube are then painted red .If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them ,how many small cubic blocks make up the large cube?

27=3×3×3
so the answer is (3+1+1)^3=125

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