  We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet
gravity with product two-spheres topology, ${\bf SO(n) \times SO(n)}$, in
higher dimensions. There is an unusual new feature of Gauss-Bonnet black hole
that the avoidance of non-central naked singularity prescribes a mass range for
black hole in terms of $\Lambda>0$. For Einstein-Gauss-Bonnet black hole a
limited window of negative values for $\Lambda$ is also permitted. This
topology encompasses black string and brane as well as a generalized Nariai
metric. We also give new solutions with product two-spheres of constant
curvatures.
