how are energy and mass connected during the formation of an atom?

they are connected by e =mc^2,  where e is the energy, m is the mass and c is speed of light , a mass m  from the atom must be converted to energy to hold the nucleons together, the mass is termed as mass defects , the energy is termed as binding energy. in technical terms , a mass m must be converted to energy E  called binding energy for  nuclei of atoms.