  In this paper we consider the additive interval functions defined on the
family $\mathcal{I}_{m}$ of all non-degenerate closed subintervals of the cubic
interval $C_{m} = [0,1]^{m}$ in the $m$-dimensional Euclidean space
$\mathbb{R}^{m}$ and taking values in a Banach space $X$. We give necessary and
sufficient conditions for an additive interval function $F : \mathcal{I}_{m}
\to X$ to be the primitive of a variational McShane (or strong McShane)
integrable function $f : C_{m} \to X$ in terms of the convex cubic average
range of $F$.
