We investigate the discovery potential of cubic-kilometer neutrino observatories such as IceCube to set stringent limits on the forbidden decays $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}{\overline{\ensuremath{\nu}}}_{e}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$. The signatures for these decays are cascade events resulting from the charged-current reactions of ${\ensuremath{\nu}}_{e}$, ${\ensuremath{\nu}}_{\ensuremath{\tau}}$, ${\overline{\ensuremath{\nu}}}_{e}$, and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ on nuclei in such detectors. Background cascade events are mainly due to ${\ensuremath{\nu}}_{e}$'s from atmospheric $\ensuremath{\mu}$, ${K}^{+}$, and ${K}_{S}^{0}$ decays and to a lesser extent from atmospheric ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ neutral-current interactions with nuclei. A direct upper limit for the branching ratio $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e,\ensuremath{\tau}}{\overline{\ensuremath{\nu}}}_{e,\ensuremath{\tau}}$ of $6.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ at 90% CL can be achieved.

We investigate the discovery potential of cubic-kilometer neutrino observatories such as IceCube to set stringent limits on the forbidden decays eta -> nu(e)(nu) over bar (e) and eta -> nu(tau)(nu) over bar (tau). The signatures for these decays are cascade events resulting from the charged-current reactions of nu(e), nu(tau), (nu) over bar (e), and (nu) over bar (tau) on nuclei in such detectors. Background cascade events are mainly due to nu(e)'s from atmospheric mu, K+, and K-S(0) decays and to a lesser extent from atmospheric nu(mu) neutral-current interactions with nuclei. A direct upper limit for the branching ratio eta -> nu(e,tau)(nu) over bar (e,tau) of 6.1 x 10(-4) at 90% CL can be achieved.