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 .