Is there a relationship between Average energy of transmission and power saving
First of all, 8 b/s/Hz is not a bit rate, but rather a spectral efficiency.

Second, you don't transmit $\log_2(M)$ bits per second, but rather $\log_2(M)$ bits per channel use, which is roughly $T_s$ seconds, where $T_s$ is the symbol time. So, the bit rate is $\frac{\log_2(M)}{T_s}$.

If you adjust your wording to the above by saying 8 bits/channel use, then, yes, you are right, you save energy by using MIMO, but the saving is $170/20$ not the reciprocal.