Gonality, apolarity and hypercubics

We show that any Fermat hypercubic is apolar to a trigonal curve, and vice versa. We show also that the Waring number of the polar hypercubic associated to a tetragonal curve of genus g is at most the ingegral part of 3/2 g − 7/2, and for a large class of them is at most 4/3 g − 3.