Apparently, a sign on a wall telling you to make a cake will suffice, so zero mods is possible.
Now, given all the things in vanilla, that can be done with redstone, custom spawner tags, command blocks, etc, zero mods is entirely possible.
Cake, for example, requires milk. If cows are regularly killed by command blocks, then getting that milk might be hard. You might have to go searching in the dungeons of infinite doom, and solve the teleporter puzzle to make it to the dispensing station where redstone verifies that you have solved the puzzles before dispensing a cow spawn egg.
I'll let someone else that knows command blocks and the scoring system far better than I do implement that one.