  In this article we find connections between the values of Gauss
hypergeometric functions and the dimension of the vector space of Hodge cycles
of four dimensional cubic hypersurfaces. Since the Hodge conjecture is
well-known for those varieties we calculate values of Hypergeometric series on
certain $CM$ points. Our methods is based on the calculation of the
Picard-Fuchs equations in higher dimensions, reducing them to the Gauss
equation and then applying the Abelian Subvariety Theorem to the corresponding
hypergeometric abelian varieties.
