Subcubic growth of the averaged Dehn function for a class 2 nilpotent group

We show that the averaged Dehn function with respect to each finite presentation of an arbitrary finitely generated class 2 nilpotent group is subcubic. For the finite rank $\geqslant2$ free class 2 nilpotent group this implies the subasymptoticity of the averaged Dehn function in the sense of M. Gromov, confirming his conjecture.