We consider the cubic di_erential system of the formx_ = y + ax2 + cxy - y2 + [(a - 1)(p + c - b) + g]x3++[(b - p)(p + c - b) - a - n - 1]x2y + pxy2;y_ = -x - gx2 - dxy - by2 + (a - 1)(d + n - 1)x3++[(b - p)(d + n + 1) - g]x2y + nxy2 + by3;(1)where the variables x = x(t); y = y(t) and coe_cients a; b; c; d; g; p; n are assumed to be real. Theorigin O(0; 0) is a singular point of a center or a focus type for (1), i.e. a _ne focus.It is easy to verify that the cubic system (1) has two invariant straight lines of the forml1 _ 1 + A1x - y = 0; l2 _ 1 + A2x - y = 0; where A1; A2 are distinct solutions of the equationsA2 + (b - c - p)A - d - n - 1 = 0, and we determine the conditions under which the cubic system(1) has also one irreducible invariant cubic curve of the form_(x; y) _ x2 + y2 + a30x3 + a21x2y + a12xy2 + a03y3 = 0with (a30; a21; a12; a03) 6= 0 and a30; a21; a12; a03 2 R. The problem of the center for cubic system(1) with: two parallel invariant straight lines and one invariant cubic _ = 0 was solved in [1]; abundle of three algebraic curves l1 = 0; l2 = 0 and _ = 0 was solved in [2].In this paper we study the problem of the center for cubic system (1) having three algebraicsolutions l1 = 0; l2 = 0, _ = 0 in generic position and prove the following theorem:Theorem 1. Let the cubic system (1) have two invariant straight lines l1 = 0; l2 = 0 and oneirreducible invariant cubic _ = 0. Then a _ne focus O(0; 0) is a center if and only if the _rst threeLyapunov quantities vanish.