  The energy distributions for a black hole solution resulting from coupling
electrodynamics and gravity in 2+1 dimensions are obtained. This solution
considers the correction for a 2+1 static charged black hole from the first
contribution of the weak field limit of one loop QED in 2+1 dimensions. The
Einstein and Moller energy-momentum prescriptions are used to evaluate the
energy distributions associated with the mentioned 2+1 dimensional black hole
and other 2+1 black hole solutions coupled with nonlinear electrodynamics. A
relation that connects the coefficients of both prescriptions is established.
