Right rectangular prism P is similar to right rectangular prism Q. The surface area of right rectangular prism P is 20 square centimeters ($c{m}^2$), and the surface area of right rectangular prism Q is 180 $c{m}^2$. The volume of right rectangular prism Q is 270 cubic centimeters ($c{m}^3$). What is the sum of the volumes, in $c{m}^3$, of right rectangular prism P and right rectangular prism Q?