  In this paper, we obtain the lower-dimensional limits $(p=2,3,4,5,6)$ of
cubic Lovelock gravity through a regularized Kaluza-Klein reduction. By taking
a flat internal space for simplicity, we also study the static black hole
solutions in the resulting theories. We show that the solutions match with the
ones obtained from the "naive limit" of $D$-dimensional equation for the metric
function, which is obtained by first scaling the relevant couplings by a factor
of $\frac{1}{D-p}$ and then taking the limit $D\to p$, with one important
exception: In 4D, one obtains the expected solution only for the black hole
with a planar horizon.
