You see, atomic masses are not determined by adding nucleon masses; for one thing, that wouldn't work any too well because of the mass changes associated with nuclear binding energies. Instead, atomic masses are determined from whole atoms, by a combination of definition and experiment.

Definition

Atomic masses are defined in terms of a reference mass; all atomic masses nowadays are determined relative to the standard mass of ¹²C = 12.00000000...

Experiment

Atomic and molecular masses are determined by mass spectrometry, in which a single electron is stripped from the species of interest and the charge/mass ratio of the resulting cation is determined. Since only a single electron is stripped away, the resulting number is essentially the same as the mass with a full complement of electrons (and can be easily corrected for the single missing electron). Thus, the electron masses are factored into the way atomic masses are determined, and the atomic masses you see on the Periodic Table include all the atom's electrons.