Answer
The constant of variation is $\frac{1}{2}$.
The variation equation is $y=\frac{1}{2}x^3$.
Work Step by Step
$y=kx^3$
$y=32; x=4$
$32=k(4)^3$
$32=k(64)$
$k=\frac{1}{2}$
$y=\frac{1}{2}x^3$
The constant of variation is $\frac{1}{2}$.
The variation equation is $y=\frac{1}{2}x^3$.