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2x + 2 is even and cube of an integer
All the even integerâ€™s cube is even and odd integerâ€™s cube is odd
(2x+2)^ 1/3 has to be even ... 8 (2^3) or 64 (4^3) or 216 (6^3) ....
So x could be 3 or 31 or 107...x is odd
Average of any x consecutive integer is an integer, only when x is odd