  To any cubic surface, one can associate a cubic threefold given by a triple
cover of $\mathbb P^3$ branched in this cubic surface. D. Allcock, J. Carlson,
and D. Toledo used this construction to define the period map for cubic
surfaces. It is interesting to calculate this map for some specific cubic
surfaces. In this paper, we have calculated it in the case when the cubic
surface is given by a triple covering of $\mathbb P^2$ branched in a smooth
elliptic curve. In this case, the periods can be expressed through periods of
the corresponding elliptic curve.
