Brillouin microlasers based on microresonators with whispering gallery modes (WGMs) are in high demand for different applications including sensing and biosensing. We fabricated a microsphere resonator with WGMs from a synthesized high-quality tellurite glass with record high Q-factors for tellurite microresonators (Q ≥ 2.5 × 107), a high Brillouin gain coefficient (compared to standard materials, e.g., silica glasses), and a Brillouin frequency shift of 9 ± 0.5 GHz. The high density of excited resonance modes and high loaded Q-factors allowed us to achieve experimentally cascade Stokes-Brillouin lasing up to the 4th order inclusive. The experimental results are supported by the results of the theoretical analysis. We also theoretically obtained the dependences of the output Brillouin powers on the pump power and found the pump-power thresholds for the first five Brillouin orders at different values of pump frequency detuning and Q-factors, and showed a significant effect of these parameters on the processes under consideration.