Good luck expanding!

Number Theory Level 5

Find the absolute value of the sum of all integral $x$ and $y$ for which the equation

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

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