The difference between lateral surface area and total surface area of a cube is $450 {\mathrm{cm}}^2$. Find the lateral and total surface areas and volume of the cube.

In the figure below, $O$ is centre of the circle and $\mathrm{OABC}$ is a square. $P$ and $Q$ are the mid-points of $\mathrm{OC}$ and $\mathrm{OA}$, respectively. The area of the square(in ${\mathrm{cm}}^2$), if the area of the shaded part is $38.5 {\mathrm{cm}}^2$, is _____.