  In this paper we present the expressions for the energy of a regular class of
exact black hole solutions of Einstein's equations coupled with a nonlinear
electrodynamics source. We calculate the energy distribution using the
Einstein, Weinberg and M{\o}ller prescriptions. We make a discussion of the
results in function of two specific parameters, a sort of dipole and quadrupole
moments of the nonlinear source $\alpha$ and $\beta$, and in addition a study
of some particular cases is performed.
