We give an explicit formula for sp2n-basic representatives of the cyclic cohomology of the Weyl algebra HC(A2n). This paper can be seen as cyclic addendum to the paper [6] by Feigin, Felder and Shoikhet, where the analogous Hochschild case was treated. As an application, we prove a generalization of a Theorem of Nest and Tsygan concerning the relation of the Todd class and the cyclic cohomology...