Your first sum gives the atomic mass of an element with only one isotope. If the element has more than one isotope you work out the mass of each isotope using your first sum and then combine them using AbundanceA*MassA + AbundanceB*MassB + AbundanceC*MassC +. making sure that all your abundances (AbundanceA + AbundanceB + AbundanceC ...) total exactly 1.
gippgig's sum is more accurate and if you add the mass of the electrons it's 'right', but it's not that helpful as the most practical method we have for finding the binding energy is to find the real mass of an isotope experimentally and then subtract everything else. Like pretty much everything in science, to approach the real answer you have to do an experiment.