  A graph is cubical if it is a subgraph of a hypercube. For a cubical graph
$H$ and a hypercube $Q_n$, $ex(Q_n, H)$ is the largest number of edges in an
$H$-free subgraph of $Q_n$. If $ex(Q_n, H)$ is equal to a positive proportion
of the number of edges in $Q_n$, $H$ is said to have positive Tur\'an density
in a hypercube; otherwise it has zero Tur\'an density. Determining $ex(Q_n, H)$
and even identifying whether $H$ has positive or zero Tur\'an density remains a
widely open question for general $H$.
  In this paper we focus on layered graphs, i.e., graphs that are contained in
an edge-layer of some hypercube. Graphs $H$ that are not layered have positive
Tur\'an density because one can form an $H$-free subgraph of $Q_n$ consisting
of edges of every other layer. For example, a $4$-cycle is not layered and has
positive Tur\'an density.
  However, in general it is not obvious what properties layered graphs have. We
give a characterisation of layered graphs in terms of edge-colorings. We show
that most non-trivial subdivisions have zero Tur\'an density, extending known
results on zero Tur\'an density of even cycles of length at least $12$ and of
length $8$. However, we prove that there are cubical graphs of girth $8$ that
are not layered and thus having positive Tur\'an density. The cycle of length
$10$ remains the only cycle for which it is not known whether its Tur\'an
density is positive or not. We prove that $ex(Q_n, C_{10})= \Omega(n2^n/ \log^a
n)$, for a constant $a$, showing that the extremal number for a $10$-cycle
behaves differently from any other cycle of zero Tur\'an density.
