What is an example of force of attraction between two objects that have mass

Technically, every particle attracts every other particle. The Shell theorem says that for spherical objects of uniform density, where neither object is inside the other, we can regard them as though all the mass of each object were located at the center of mass of that object.

The Shell Theorem may apply to forces besides gravity, (notably the Coulomb Force) but it would be the center of charge, rather than the center of gravity.