Let's consider that an object has a uniform mass
The center of surface is
$$\vec C_s=\frac{\iint_{\mathbb{S}} \vec rdS}{\iint_{\mathbb{S}} dS}$$
And the center of mass is
$$\vec C_v=\frac{\iiint_{\mathbb{V}} \vec rdV}{\iiint_{\mathbb{V}} dV}$$
For a sphere or a cube, both result the same point.
I am wondering,
1- For which objects are they necessarily the same?
2- For a CAD design which is described by surface triangles, calculating $\vec C_v$ is hard. Is $\vec C_s$ a good approximation?
Center of mass and center of surface necessarly coincide for symmetric object like spheres, cubes, cylinder indeed in these cases the center of mass coincides with a center of symmetry. Otherwise it is not necessarly true and the approximation could not be so good.