  Within the framework of four-dimensional quadratic curvature gravities in the
appearance of a negative cosmological constant, a definition for the
gravitational energy of solutions with anti-de Sitter (AdS) asymptotics was put
forward in Ref. [1]. This was achieved by adding proper topological invariant
terms to the gravity action to render the variation problem well-posed. In the
present note, we prove that the definition via the procedure of topological
regularization can be covered by the one given in Ref. [3] in four dimensions.
Motivated by this, we further generalize the results to generic gravity
theories in arbitrary even dimensions.
