  A $(m+ 3)$-dimensional Einstein-Gauss-Bonnet gravitational model including
the Gauss-Bonnet term and the cosmological term $\Lambda$ is considered. Exact
solutions with exponential time dependence of two scale factors, governed by
two Hubble-like parameters $H >0$ and $h \neq H$, corresponding to factor
spaces of dimensions $m >2$ and $l = 2$, respectively, are found. Under certain
restrictions on $x = h/H $, the stability of the solutions in a class of
cosmological solutions with diagonal metrics is proved. A subclass of solutions
with small enough variation of the effective gravitational constant $G$ is
considered and the stability of all solutions from this subclass is shown.
