  We study the discrete spectrum of the Robin Laplacian $Q^{\Omega}_\alpha$ in
$L^2(\Omega)$, \[ u\mapsto -\Delta u, \quad \dfrac{\partial u}{\partial
n}=\alpha u \text{ on }\partial\Omega, \] where $\Omega\subset \mathbb{R}^{3}$
is a conical domain with a regular cross-section $\Theta\subset \mathbb{S}^2$,
$n$ is the outer unit normal, and $\alpha>0$ is a fixed constant. It is known
from previous papers that the bottom of the essential spectrum of
$Q^{\Omega}_\alpha$ is $-\alpha^2$ and that the finiteness of the discrete
spectrum depends on the geometry of the cross-section. We show that the
accumulation of the discrete spectrum of $Q^\Omega_\alpha$ is determined by the
discrete spectrum of an effective Hamiltonian defined on the boundary and far
from the origin. By studying this model operator, we prove that the number of
eigenvalues of $Q^{\Omega}_\alpha$ in $(-\infty,-\alpha^2-\lambda)$, with
$\lambda>0$, behaves for $\lambda\to0$ as \[ \dfrac{\alpha^2}{8\pi \lambda}
\int_{\partial\Theta} \kappa_+(s)^2d s +o\left(\frac{1}{\lambda}\right), \]
where $\kappa_+$ is the positive part of the geodesic curvature of the
cross-section boundary.
