  We construct a unilateral lattice tiling of $\mathbb{R}^n$ into hypercubes of
two differnet side lengths $p$ or $q$. This generalizes the Pythagorean tiling
in $\mathbb{R}^2$. We also show that this tiling is unique up to symmetries,
which proves a variation of a conjecture by B\"olcskei from 2001. For positive
integers $p$ and $q$ this tiling also provides a tiling of
$(\mathbb{Z}/(p^n+q^n)\mathbb{Z})^n$.
