The mass of a nucleus consisting of A nucleons is not entirely determined by the masses of the nucleons. The difference (the ``mass defect'') is the binding energy: that energy required to disassemble the nucleus. Note that the mass is defined in terms of atomic masses (it includes the electron masses).
The binding energy contributes significantly ( ) to the mass of a nucleus. This implies that the constituents of two (or more) nuclei can be rearranged to yield a different and perhaps greater binding energy and thus points towards the existence of nuclear reactions in close analogy with chemical reactions amongst atoms.