  A visibility representation of a graph $G$ is an assignment of the vertices
of $G$ to geometric objects such that vertices are adjacent if and only if
their corresponding objects are "visible" each other, that is, there is an
uninterrupted channel, usually axis-aligned, between them. Depending on the
objects and definition of visibility used, not all graphs are visibility
graphs. In such situations, one may be able to obtain a visibility
representation of a graph $G$ by allowing vertices to be assigned to more than
one object. The {\it visibility number} of a graph $G$ is the minimum $t$ such
that $G$ has a representation in which each vertex is assigned to at most $t$
objects.
  In this paper, we explore visibility numbers of trees when the vertices are
assigned to unit hypercubes in $\mathbb{R}^n$. We use two different models of
visibility: when lines of sight can be parallel to any standard basis vector of
$\mathbb{R}^n$, and when lines of sight are only parallel to the $n$th standard
basis vector in $\mathbb{R}^n$. We establish relationships between these
visibility models and their connection to trees with certain cubicity values.
