As shown above by @Michal_Adamaszek
xy^2\geq z^3 with x,y,z\geq 0 is equivalent to sy\geq z^2,\ xz\geq s^2.
The latter can be written in CVX as
variables x y z s
{z,s,y} == rotated_lorentz(1)
{s,x,z} == rotated_lorentz(1)
Then use x in place of z^3/y^2