  We calculate non-Gaussianities in the bispectrum and trispectrum arising from
the cubic term in the local expansion of the scalar curvature perturbation. We
compute to three-loop order and for general momenta. A procedure for evaluating
the leading behavior of the resulting loop-integrals is developed and
discussed. Finally, we survey unique non-linear signals which could arise from
the cubic term in the squeezed limit. In particular, it is shown that loop
corrections can cause $f_{NL}^{sq.}$ to change sign as the momentum scale is
varied. There also exists a momentum limit where $\tau_{NL} <0$ can be
realized.
