  The evaluation of the energy-momentum distribution for a new
four-dimensional, spherically symmetric, static and charged black hole
spacetime geometry with constant non-zero topological Euler density is
performed by using the energy-momentum complexes of Einstein and M{\o}ller.
This black hole solution was recently developed in the context of the coupled
Einstein--non-linear electrodynamics of the Born-Infeld type. The energy is
found to depend on the mass $M$ and the charge $q$ of the black hole, the
cosmological constant $\Lambda$ and the radial coordinate $r$, while in both
prescriptions all the momenta vanish. Some limiting and particular cases are
analyzed, illustrating the rather extraordinary character of the spacetime
geometry considered.
