  Using recently developed efficient symbolic manipulations tools, we present a
general gauge-invariant formalism to study arbitrary radiative $(l\geq 2)$
second-order perturbations of a Schwarzschild black hole. In particular, we
construct the second order Zerilli and Regge-Wheeler equations under the
presence of any two first-order modes, reconstruct the perturbed metric in
terms of the master scalars, and compute the radiated energy at null infinity.
The results of this paper enable systematic studies of generic second order
perturbations of the Schwarzschild spacetime. In particular, studies of
mode-mode coupling and non-linear effects in gravitational radiation, the
second-order stability of the Schwarzschild spacetime, or the geometry of the
black hole horizon.
