  We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in
the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations
exhibit unstable modes for small black holes. We call this the mass-induced
instability of SAdS black hole because the instability of small black holes
arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but
not a feature of higher-order derivative theory giving ghost states. Also, we
point out that the correlated stability conjecture holds for the SAdS black
hole by computing the Wald entropy of SAdS black hole in Einstein-Ricci cubic
gravity.
