Discrete signals: Power and Energy after Up/Downsampling
Your basic mistake is that power is energy per sample.  Power is energy per time.  In other words, P = E/t, not P = E/N as you used.

Resampling at a different rate doesn't change the time duration of the signal (t in the equation above).  Resampling at a lower sample rate, for example, decreases the number of sample, but also increases the energy per sample.