  We show that the vertices and edges of a $d$-dimensional grid graph $G=(V,E)$
($d\geqslant 2$) can be labeled with the integers from $\{1,\ldots,\lvert
V\rvert\}$ and $\{1,\ldots,\lvert E\rvert\}$, respectively, in such a way that
for every subgraph $H$ isomorphic to a $d$-cube the sum of all the labels of
$H$ is the same. As a consequence, for every $d\geqslant 2$, every
$d$-dimensional grid graph is $Q_d$-supermagic where $Q_d$ is the $d$-cube.
