  We consider the generic massless cubic gravities coupled to a negative bare
cosmological constant mainly in $D=5$ and $D=4$ dimensions, which are Einstein
gravity extended with cubic curvature invariants where the linearized excited
spectrum around the AdS background contains no massive modes. The generic
massless cubic gravities are more general than Myers quasi-topological gravity
in $D=5$ and Einsteinian cubic gravity in $D=4$. It turns out that the massless
cubic gravities admit the black holes at least in a perturbative sense with the
coupling constants of the cubic terms becoming infinitesimal. The first order
approximate black hole solutions with arbitrary boundary topology $k$ are
presented, and in addition, the second order approximate planar black holes are
exhibited as well. We then establish the holographic dictionary for such
theories by presenting $a$-charge, $C_T$-charge and energy flux parameters
$t_2$ and $t_4$. By perturbatively discussing the holographic R\'enyi entropy,
we find $a$, $C_T$ and $t_4$ can somehow determine the R\'enyi entropy with the
limit $q\rightarrow 1$, $q\rightarrow 0$ and $q\rightarrow \infty$ up to the
first order, where $q$ is the order of the R\'enyi entropy. For holographic
hydrodynamics, we discuss the shear-viscosity-entropy-ratio and find that the
patterns deviating from the KSS bound $1/(4\pi)$ can somehow be controlled by
$((c-a)/c,t_4)$ up to the first order in $D=5$, and
$((\mathcal{C}_T-\tilde{a})/\mathcal{C}_T,t_4)$ up to the second order in
$D=4$, where $\mathcal{C}_T$ and $\tilde{a}$ differ from $C_T$-charge and
$a$-charge by inessential overall constants.
