Listed below are some advanced tips and hints for solving the 4 squares:
Solve difficult bits before easy bits. A corner/edge pair is more difficult to form than a centre/edge pair, and an outer square is more difficult to form than an inner square.
Always store blocks in their best fit position, so as not to obstruct further movement of pieces.
If you see a difficult block already built, or partially built (e.g. pieces aligned but not joined), then make use of it. If you can't make use of it immediately, then try to preserve it (i.e. store it in a best fit position) while solving other parts of the cube.
Try to take advantage of the current state of the cube. For example, in choosing an outer square for your first square, there are 24 different possible squares you could choose from. Pick one that is already partially (or fully) built. For the second square, it is usually best to build the adjacent inner square with matching colours. This will give you 9 possible squares to choose from for building the third square.
Of the 9 possible third squares, 3 match in colour, while 6 do not match. There is not much difference between choosing a matching or non-matching one, so again pick whichever square is closest to being fully built. If you pick one of the squares with matching colours, you will have 4 squares to choose from for the fourth square.
If, on the other hand, you pick one of the non-matching squares as your third square, you will have one square to choose from for the fourth square. In the following example, the fourth square must be the yellow/orange/blue square:
There is, however, an alternative to building a fourth square:
The separate corner/edge pair has the right colours to form part of stage 1, but the centre/edge pair it needs to join with to form a square is already being used in a different square.
We can still make use of this corner/edge pair by joining it onto the existing square to form a rectangle.
Click the play button to view the procedure.
Fortunately there are efficient ways to insert the remaining edge.
Click the play button to see the edge inserted.