Period-one (P1) oscillations in semiconductor lasers are applicable in photonic millimeter-wave (mm-wave) generation. P1 oscillation can be invoked by optically injecting a laser, where the phase noise can be suppressed by modulation. To increase the frequency range of mm-wave generation, cascaded injection is investigated for enhancing the P1 oscillation harmonics. Relative to the optical frequency of the injection from a master laser, P1 oscillation at frequency f0 is induced in a primary slave laser which, in turn, injects a secondary slave laser for enhancing the harmonic at 2f0. Experimentally, photonic mm-wave generation at 2f0=72 GHz is demonstrated using P1 oscillations at f0=36 GHz. Subharmonic locking by modulation at f0/4=9 GHz can suppress the output phase noise to -87 dBc/Hz at 10 kHz offset. The mm-wave power can be strengthened by the coherent addition from the master laser. The mm-wave frequency can be tuned by varying the operating conditions of the lasers. Extension to higher frequencies is possible using the approach of cascaded injection.