  Kamke \cite{Kamke1921} solved an analog of Waring's problem with $n$th powers
replaced by integer-valued polynomials. Larsen and Nguyen \cite{LN2019}
explored the view of algebraic groups as a natural setting for Waring's
problem. This paper applies the theory of polynomial maps and polynomial
sequences in locally nilpotent groups developed in previous work \cite{Hu2020}
to solve an analog of Waring's problem for the general discrete Heisenberg
groups $H_{2n+1}(\mathbb{Z})$ for any integer $n\ge1$.
