The density of iron is 7g/cc, the density of copper is 9g/cc
Let's assume that the average density is 7g/cc (using square section copper and as many tricks as we can manage to reduce the volume of anything other than iron or copper in the transformer).
Assuming a weight of 500g, that means the volume will be at least 72cc. That's about 4.5 cubic inches, so you'll never find anything less than about 1.7 inches per side (assuming it's cubic)