  We present a streamlined proof that any Einstein-AdS space is a solution of
the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction
of conformal gravity into Einstein theory manifestly shows that the action of
the latter can be written as the Einstein-Hilbert term plus the Euler
topological density and an additional contribution that depends on the
Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this
form of the action by embedding the Einstein theory into a Weyl-invariant
purely metric theory, was dubbed Conformal Renormalization and its resulting
action was shown to be equivalent to the one obtained by holographic
renormalization. As a non-trivial application of the method, we compute the
Noether-Wald charges and thermodynamic quantities for topological black hole
solutions with generic transverse section in Einstein-AdS$_6$ theory.
