Good luck expanding!

Find the absolute value of the sum of all integral xx and yy for which the equation

x3+(x+1)3+(x+2)3+(x+3)3++(x+7)3=y3x^3+(x+1)^3+(x+2)^3+(x+3)^3+\dots+(x+7)^3=y^3

is satisfied. As an explicit example, if the solutions were (3,7)(3, 7) and (9,9)(9, 9), you would be asked to find 3+7+9+93+7+9+9.

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