Is it possible to calculate specific heat capacity of a compound based on its elements' heat capacities?
There is not much connection between the heat-capacity of a compound and the heat-capacity of the elements it is made of. Heat capacity is primarily coming from the low frequency vibrations of the lattice (if it is solid), and vibration+rotation+translation if it is liquid or gas. These have no connection with the properties of the lattice etc properties of the given elements.

So short answer: no