  We provide integral formulae for the ADM mass of asymptotically flat
hypersurfaces in Riemannian manifolds with a certain warped product structure
in a neighborhood of infinity, thus extending Lam's recent results on Euclidean
graphs to this broader context. As applications we exhibit, in any dimension,
new classes of manifolds for which versions of the Positive Mass and Riemannian
Penrose inequalities hold and discuss a notion of quasi-local mass in this
setting. The proof explores a novel connection between the co-vector defining
the ADM mass of a hypersurface as above and the Newton tensor associated to its
shape operator, which takes place in the presence of an ambient Killing field.
