  We consider $10$-dimensional gravitational model with $SO(6)$ Yang-Mills
field, Gauss-Bonnet term and $\Lambda$-term. We study so-called cosmological
type solutions defined on product manifold $M = R \times R^3 \times K$, where
$K$ is $6d$ Calabi-Yau manifold. By putting the gauge field 1-form to be
coinciding with 1-form spin connection on $K$, we obtain exact cosmological
solutions with exponential dependence of scale factors (upon $t$-variable),
governed by two non-coinciding Hubble-like parameters: $H >0$, $h$, obeying $ H
+ 2 h \neq 0$. We also present static analogs of these cosmological solutions
(for $H \neq 0$, $h \neq H$ and $ H + 2 h \neq 0$). The islands of stability
for both classes of solutions are outlined.
