  We construct an approximate solution to the cosmological perturbation theory
around Einstein-de Sitter background up to the fourth-order perturbations. This
could be done with the help of the specific symmetry condition imposed on the
metric, from which follows, that the model density forms an infinite, cubic
lattice. We show that the perturbative solution obtained this way can be
interpreted as the exact solution to the Einstein equations for a dust-like
energy-momentum tensor. In our model, it seems that physical quantities
averaged over a large scales overlap with the respective Einstein-de Sitter
prediction, while local observables could differ significantly from their
background counterparts. As an example, we analyze in details a behaviour of
the local and the global measurements of the Hubble constant, which is
important in the context of a current Hubble tension problem.
