Some of the strongest currently-known subconvex bounds are for L-functions of cusp forms twisted by quadratic characters and are due to Conrey and Iwaniec. Their estimate is derived from an estimate of the cubic moment of these L-functions. I will present a Motohashi-type formula which describes the dual sums of this cubic moment. This Motohashi formula is crucial in extending Conrey and Iwaniec's results to the particularly challenging case of weight 2 cusp forms.