Abstract
In [12], a theory that is equal to Einstein’s gravity up to the third order in curvature in the linear limit of field equations in a vacuum which is called Einsteinian cubic gravity has been introduced. This theory contains Einstein’s standard term, cosmological constant, Gauss-Bonnet and third order curvature terms.
In this paper, we will find answers of this theory in four dimensions, in which space and time behave differently under the scale conversions. To find these kind of solutions, We used the Lifshitz metric with hyperscaling violation with θ and showed that in cubic gravity, the are black hole solutions with hyperscaling violation  for any arbitrary value of z and only for θ = 2 in four dimensions. Also we will see that for this black hole thermodynamic quantities such as temprature and entropy are zero.