Finding $c$ with Dulong-Petit law on non-molecular substance
It may be useful to start with the specific molar heat capacity $c'$ (per mole, instead of per kilogram), which is somewhat more fundamental. Here $c' = 3R$. 

This is true even for your crystalline solid, though we have to decide what "moles" refers to in this case. From a physical perspective, the heat capacity is a result of vibrational motion in three dimensions, and each atom will contribute to this motion. Our "moles" should therefore be "moles of atoms"---for the purposes of this calculation, we consider the atom to be the fundamental unit.

The molar mass should then be $\text{mass of solid/moles of atoms}$, which can be interpreted as a weighted molar mass. You can see that your formula $M/n$ calculates exactly this: the mass per mole of a formula unit, divided by the number of atoms in a formula unit. 

Hence $$c = \frac{3R}{M/n} = \frac{3R}{M}n.$$