We consider the real cubic system of differential equations x˙ = y + ax2 + cxy + fy2 + kx3 + mx2y + pxy2 + ry3 ≡ p (x, y) , y˙ = −(x + gx2 + dxy + by2 + sx3 + qx2y + nxy2 + ly3) ≡ q (x, y) , gcd(p, q) = 1, sx4 + (k+q)x3y + (m+n)x2y2 + (l+p)xy3 + ry4 ̸≡ 0 (1) and the homogeneous system associated to the system (1): {x˙ = P (x, y,Z) , y˙ = Q(x, y,Z)}, where P (x, y,Z) = yZ2 + (ax2 + cxy + fy2)Z + kx3 + mx2y + pxy2 + ry3, Q(x, y,Z) = −(xZ2 + (gx2 + dxy + by2)Z + sx3 + qx2y + nxy2+ +ly3). Denote X∞=P (x, y,Z) ∂ ∂x + Q(x, y,Z) ∂ ∂y . The linearized system (1) in critical point (0, 0) has a center in this point, i.e. (0, 0) is a linear center for (1). We say that for (1) the line at infinity Z = 0 has multiplicity ν + 1 if ν is the greatest positive integer such that Zν divides E∞ = PX∞(Q) − QX∞(P))[1]. Theorem 1. In the class of cubic differential systems of the form (1) the maximal multiplicity of the line at infinity is five.Theorem 2. The system (1) has the line at infinity of multiplicity five if and only if its coefficients verify one of the following three set of conditions: C = D = 0, B = −AS3/K3, F = −AS2/K2, G= AS/K, M = S, L = −S4/K3, N = R = −S3/K2, Q= −P = S2/K; (2) A=5F3/B2,C=−6F2/B,D=2F,G=−3F2/B,K=F5/B3,L=BF, M=−3F4/B2,N=−3F2,P=Q=3F3/B,R=−F2,S=−F4/B2, S ̸= 0; (3) A = −K2(2BK − 3FS)/S3,C = −2K(BK − 2FS)/S2,D = 2F, G = K(2FS − BK)/S2,L = S4/K3,M = 3S,N = 3S3/K2, P = 3S2/K,Q = 3S2/K,R = S3/K2, K2(BK − FS)2 + 4S5 = 0, (4) where A = g − b − c + i(a + d − f), C = 2(b + g + i(a + f)), F = c + g − b + i(a − d − f), K = r + s − m − n + i(k − l − p + q), M = n − m − 3(r − s) + i(3(k + l) + p + q), P = m + n + 3(r + s) + i(3(k − l) + p − q), R = m − n − r + s + i(k + l − p − q), B = A, D = C, G = F, L = K, N = M, Q = P, S = R, (5)