Question $2$ Worth $8$ points $$

Convert this integral from rectangular coordinates to spherical coordinates $($Do not evaluate the integral$)$

${\displaystyle \underset{-a}{\overset{a}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{a^2-y^2}}{\overset{\sqrt[\phantom{2}]{a^2-y^2}}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{a^2-x^2-y^2}}{\overset{\sqrt[\phantom{2}]{a^2-y^2}}{}}}(x^{2}z+y^{2}z+z^3)dzdxdy.$