E=mc2 converts from kg to joules. True, the units aren't in the same class (energy and mass), unlike my example with inches to centimeters. But it's still just a conversion of sorts. It would be like converting from mass to volume for a given substance, e.g. 1kg of water at ~40C is 1 liter.
So when Einstein says that mass and energy are the same, is he saying that length and time are the same? It's like Einstein has mass = energy and length = time and now you present mass = volume. It's interesting that volume is length3, so your univers must be a co-universe to Einstein's, where mass = length and energy = time and the density of water is a universal constant.
OK, I see the error I'm making. It's not saying that the mass is energy, just that it can be converted to that much energy. So my comparisons to say length conversion are wrong. Still the point is that the c2 is just a conversion factor. Essentially it's just saying that mass is a form of energy, and c2 part gets the value and units correct.
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