Let's say hypothetically I wanted to raise a pokemon from level 1
allll the way to 250 using mainly powerorbs from the exp share (I
say mainly because getting interactions is sort of inevitable).

Is there a known formula for how much exp a pokemon needs to go
from one level to the next that I could use to calculate the number
of powerorbs I'd need to accomplish my hypothetical goal? Or is
there anyone who by some odd stroke of luck would happen to know
the answer (or a related answer, such as how many it would take to
get to level 100)?

I dont think there is a formula for that, but like what
Taavi said, u can see how much exp is needed for a pokemon to reach
lv100 by looking at its pokedex entry