  We investigate sufficient conditions under which cubic gravity is healthy and
viable at the perturbation level. We perform a detailed analysis of the scalar
and tensor perturbations. We impose the requirement that the two scalar
potentials, whose ratio is the post-Newtonian parameter $\gamma$, should
deviate only minimally form general relativity. Additionally, concerning tensor
perturbations we impose satisfaction of the LIGO-VIRGO and Fermi Gamma-ray
Burst observations, and thus we result to a gravitational-wave equation with
gravitational-wave speed equal to the speed of light, and where the only
deviation from general relativity appears in the dispersion relation.
Furthermore, we show that cubic gravity exhibits an effective Newton's constant
that depends on the model parameter, on the background evolution, and on the
wavenumber scale. Hence, by requiring its deviation from the standard Newton's
constant to be within observational bounds we extract the constraints on the
single coupling parameter $\beta$.
