I have three squares arranged in an inverted L shape, but the one in the middle is slightly larger than the other two squares. (Please look at the picture given below)
Further to comments clarifying your problems, here's a demonstration. Using this method the size of the squares or rectangles doesn't matter. I've deliberately shown rectangles of different sizes. I use guides and snapping to ensure an exact fit.
Begin with two over lapping squares or rectangles, and drop guides where the black square will be placed. With the snapping enabled, the guides will snap to the edges of the shapes. When you draw the black square it will snap to the guides. In this example I've also shown the snapping options I enabled.