  We derive a universal expression for the gravitational radiation energy
spectrum $dE^{GW}/d\omega$ at sub-leading order emitted from a generic
gravitational hard scattering of multi-particles or multi-bodies. Our result
includes all $\mathcal{O}(\omega)$ corrections to the gravitational radiation
flux from a generic $2\rightarrow N$ collision, in both the cases of massless
and massive particles/bodies. We also show the dependence of the radiation
energy fluxby the quantum spin in case of particle collisions. Then, we
consider the specific case of a gravitational elastic scattering of two massive
bodies, i.e. $m+M\rightarrow m+M$ with $m,M$ the masses of the two bodies
respectively. We demonstrate that in this case all $\mathcal{O}(\omega)$
contributions to the energy flux exactly cancel each others. Nevertheless, we
also show that, for a $2\rightarrow 2$ inelastic scattering, the inclusion of
sub-leading soft gravitons leads to a not zero radiation flux, having a simple
expression in certain asymptotic regimes. Our results can be applied to the
case of Black Holes' collisions with possible testable implications in
gravitational waves physics.
