  In this note, we prove the existence of a secondary term in the asymptotic
formula of the cubic moment of quadratic Dirichlet L-functions
$$\sum_{\substack{d - \mathrm{monic \, \& \, sq. \, free} \mathrm{deg}\, d \, =
\, D}} L\big(\tfrac{1}{2}, \chi_{d}\big)^{3}$$ over rational function fields on
the order of $q^{\scriptscriptstyle \frac{3}{4} D}.$ This term is in perfect
analogy with the $x^{\scriptscriptstyle \frac{3}{4}}$-term indicated in our
joint work arXiv:math/0110092v1 for the corresponding asymptotic formula over
the rationals.
