An ab initio coupled perturbed Hartree-Fock study has been performed to investigate the hyperpolarizabilities beta of a series of heteroaromatic-substituted sym-triazines in the frame of a tensorial formalism. Effects of donor or acceptor substitution and electron correlation on the octupolar triazines have also been explored. Geometric effects have been considered in a set of calculations by using fully optimized and planar structures. It is found that the effects of the deviations from the planarity on beta are very small. Octupolar triazines containing pyrrole. derivatives have larger beta than the corresponding analogues containing furan and thiophene. derivatives, and NO2 or NH2 substitution strongly affects beta of octupolar benzene-substituted triazine. An additive model is introduced to evidence specific contributions to beta arising from the multipolar symmetry. The beta tensor of a multipolar system is dissected into two separate tensor representation, an additive term beta (A) representing the tensorial sum of the dipole units' beta and a term beta (I) representing interactions between the dipole units constituting the multipole. The results indicate that when the acceptor groups (NO2) are introduced into octupolar triazines containing pyrrole and furan derivatives, the effects of the interaction term exceed that of the additive term and greatly enhance the magnitudes of beta, contrasted with unsubstitution. It is also seen that incorporating the donor groups (NH2) into the octupolar molecules not only significantly enhances beta (A) but also beta (I), compared with unsubstitution and NO2 substitution. The electron correlation has a large influence on the magnitude of the hyperpolarizabilities.