Heise method

Since we have already built the "one and only" inner square, the 3rd square must be another outer square. We can use the same techniques to build it that we used to build the first outer square.

In the example below, the first two moves form a corner/edge pair, the next move moves this pair out of the way, the following move forms a centre/edge pair, the next two moves join these pairs to form the outer square, and the final move fits this new square onto the existing white block so that it will be kept out of the way for the steps that follow.

While the 3rd square can always be built without ever breaking the existing white block, sometimes there are shortcut solutions that involve temporarily breaking this block and then restoring it: