We have
Side of the cube is 2y^2 feet.
Then, The volume of a cube is given by
[tex]V=s^3[/tex]Where s = side = 2y^2
So:
[tex]V=(2y^2)^3[/tex]Apply the exponent law
[tex]\begin{gathered} V=2^3\cdot(y^2)^3 \\ V=8(y^2)^3 \end{gathered}[/tex]Apply the property of exponents
[tex]V=8(y^{2\cdot3})[/tex]Multiply
[tex]V=8(y^6)[/tex]Answer: The volume is
[tex]8y^6[/tex]