  We constructed a simple cosmological model which approximates the Einstein-de
Sitter background with periodically distributed dust inhomogeneities. By taking
the metric as a power series up to the third order in some perturbative
parameter $\lambda$, we are able to achieve large values of the density
contrast. With a metric explicitly given, many model properties can be
calculated in a straightforward way which is interesting in the context of the
current discussion concerning the averaging of the inhomogeneities and their
backreaction in cosmology. Although the Einstein-de Sitter model can be thought
as the model \emph{average}, the light propagation differs from that of the
Einstein-de Sitter. The angular diameter distance-redshift relation is affected
by the presence of inhomogeneities and depends on the observer's position. The
model construction scheme enables some generalizations in the future, so the
present work is a step towards more realistic cosmological model described by a
relatively simple analytical metric.
