  We investigate the classical gravitational tests for the six-dimensional
Kaluza-Klein model with spherical (of a radius $a$) compactification of the
internal space. The model contains also a bare multidimensional cosmological
constant $\Lambda_6$. The matter, which corresponds to this ansatz, can be
simulated by a perfect fluid with the vacuum equation of state in the external
space and an arbitrary equation of state with the parameter $\omega_1$ in the
internal space. For example, $\omega_1=1$ and $\omega_1=2$ correspond to the
monopole two-forms and the Casimir effect, respectively. In the particular case
$\Lambda_6=0$, the parameter $\omega_1$ is also absent: $\omega_1=0$. In the
weak-field approximation, we perturb the background ansatz by a point-like
mass. We demonstrate that in the case $\omega_1>0$ the perturbed metric
coefficients have the Yukawa type corrections with respect to the usual
Newtonian gravitational potential. The inverse square law experiments restrict
the parameters of the model: $a/\sqrt{\omega_1}\lesssim 6\times10^{-3}\
{{cm}}$. Therefore, in the Solar system the parameterized post-Newtonian
parameter $\gamma$ is equal to 1 with very high accuracy. Thus, our model
satisfies the gravitational experiments (the deflection of light and the time
delay of radar echoes) at the same level of accuracy as General Relativity. We
demonstrate also that our background matter provides the stable
compactification of the internal space in the case $\omega_1>0$. However, if
$\omega_1=0$, then the parameterized post-Newtonian parameter $\gamma=1/3$,
which strongly contradicts the observations.
