  In this paper, we construct Adams-Hilton models for the polyhedral products
of spheres $(\underline{S})^{\mathcal{K}}$ and Davis-Januszkiewicz spaces
$\left(\mathbb{C} P^{\infty}\right)^{\mathcal{K}}$. We show that in these cases
the Adams-Hilton model can be chosen so that it coincides with the cobar
construction of the homology coalgebra. We apply the resulting models to the
study of iterated higher Whitehead products in $\left(\mathbb{C}
P^{\infty}\right)^{\mathcal{K}}$. Namely, we explicitly construct a chain in
the cobar construction representing the homology class of the Hurewicz image of
a Whitehead product.
