Theoretically you only need one draw call per plane though, right?

Imagine using a stack of divs like this: https://hcgilje.files.wordpress.com/2011/01/stack.png

If each of those stacked divs represents the faces of all the 16x16 cubes in that plane, then you'd only need 48 draw calls in total. The hard part would be baking the cube textures in to a giant 'megatexture' the first place, but that could be prerendered if you didn't need animation. You'd actually need 96 images because each 'layer' would need 2 sides, but I don't see why it wouldn't work.