  We extend Maldacena's argument, namely, obtaining Einstein gravity from
Conformal Gravity, to six dimensional manifolds. The proof relies on a
particular combination of conformal (and topological) invariants, which makes
manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by
taking generalized Neumann boundary conditions, the Conformal Gravity action
reduces to the renormalized Einstein-AdS action. These restrictions are implied
by the vanishing of the traceless Ricci tensor, which is the defining property
of any Einstein spacetime. The equivalence between Conformal and Einstein
gravity renders trivial the Einstein solutions of 6D Critical Gravity at the
bicritical point.
