At this stage, it becomes quite difficult to add another square without destroying what has been built so far. In fact, some situations will be impossible to solve unless we (temporarily) destroy and restore an existing block.
In the following case, the 4th square can be solved without destroying the white block:
However, in the following case, the 4th square can only be solved by temporarily destroying the white block:
Depending on which colours you chose for each square, at the end of this stage you will end up with a cube similar to one of the following:
Each of the above examples uses only 5 colours. If your squares involve all 6 colours, then you have made a mistake somewhere.