Einsteinian cubic gravity provides a holographic toy model of a
nonsupersymmetric CFT in three dimensions, analogous to the one defined by
Quasi-topological gravity in four. The theory admits explicit non-hairy AdS4​
black holes and allows for numerous exact calculations, fully nonperturbative
in the new coupling. We identify several entries of the AdS/CFT dictionary for
this theory, and study its thermodynamic phase space, finding interesting new
phenomena. We also analyze the dependence of R\'enyi entropies for disk regions
on universal quantities characterizing the CFT. In addition, we show that
η/s is given by a non-analytic function of the ECG coupling, and that the
existence of positive-energy black holes strictly forbids violations of the KSS
bound. Along the way, we introduce a new method for evaluating Euclidean
on-shell actions for general higher-order gravities possessing second-order
linearized equations on AdS(d+1)​. Our generalized action involves the very
same Gibbons-Hawking boundary term and counterterms valid for Einstein gravity,
which now appear weighted by the universal charge a∗ controlling the
entanglement entropy across a spherical region in the CFT dual to the
corresponding higher-order theory.Comment: 59 pages, 7 figures, 1 table; v4: typos fixe