Did Einstein discover E = mc^2?

One thing that bothers me about the “somebody had mc^2 and only had the proportionality constant wrong” arguments is that it ignores one very important point: whatever you come up with, the units have to be that of energy. So it’s not like the Far Side cartoon where Einstein has written E=mc^3, E=mc^7 and various other powers and the cleaning lady says “Everything’s squared away. Yessir, squaaaaaared away!” (and Albert has a wonderful look on his face). Funny, for a cartoon, but in reality you need a speed squared term to go along with mass in order to get units of energy. E=mc^7 doesn’t have units of energy. E=mc^2 does. So, really, showing what the proportionality factor is is really the majority of the battle.