  Recently discovered photonic higher-order topological insulators enable
unprecedented flexibility in the robust localization of light in structures of
different dimensionality. While the potential of the two-dimensional systems is
currently under active investigation, only a few studies explore the physics of
the three-dimensional higher-order topological insulators. Here we propose a
three-dimensional structure with cubic symmetry featuring a zero-dimensional
corner state mediated by the long-range interactions. We trace the evolution of
the corner state with the next-nearest-neighbor coupling strength and prove the
topological origin of the corner mode calculating the associated topological
invariant. Our results thus reveal the potential of long-range couplings for
the formation of three-dimensional higher-order topological phases.
