It is calculated the amplitudes of the deep-inelastic lepton scatterings off the nucleon for the color SU(3) gauge currents under the assumption of the Han-Nambu integrally-charged quark model of SU(3)×SU(3). The structure function sum rules are derived in two ways. The equal-time evaluation of the amplitudes exhibits a contribution which comes from the spin-1 color octet gluons. Evaluated on the light-cone with the decomposition which Jackiw, Van Royen and West constructed, the color octet gluons do not effect the amplitudes so that the ordinary structure function sum rules are regained. Our results can be generalized for any quark model of integral charge. Thus we conclude that the color symmetry does not deviate those relations acquired from current algebra or parton theory between structure functions on the light-cone.
