What's the max amount of blocks that can be placed of each type of block in Minecraft, not including mob spawners
There is no such limit. Although because the Far Lands exist, if you consider them the boundary of any given world; I guess the answer would be [25,101,642 * 25,101,642 * 256] or 161,303,662,360,617,984
Although you can still place blocks inside the far lands. The limit beyond which lighting and block physics cease to function is at X/Z +-32,000,000, so it could be as much as [64,000,000 * 64,000,000 * 256] or 1,048,576,000,000,000,000
(Not counting the fact that you can also place blocks in the Nether and the End, which both have similarly huge 'limits')
But beyond that, there isn't really a limit. If you are in creative mode you can place as much of what you want where you want. If you are in survival things are a little tricky, as you have renewable resources (that which you can continually generate - wood, cobblestone, wool), plentiful resources (that which exists in large quantities - dirt, sand, non-basic-stones), and limited resources (it's a vast world and there's probably more than you need, but it'll take time and effort - Diamond blocks, glowstone).