The 4 packing takes up 100% of its square; it's trivially optimal. The 6 packing only takes up 2/3 of it, so it's not necessarily obvious that you can't do better.
for me it is obvious. If I am reading s=3 as multiplier of side of smaller square to side of bigger square, which means that bigger square side is 3 times the side of smaller one, than it is obvious that it should be poossible to squeeze 9 small squares into bigger square. It is children puzzle after all. What is not obvious here?
Because it could be possible, as we just saw with 5, that by some rotation of some number of cubes, you could fit six unit cubes in to box smaller than area 9. Since we just saw the unusual result in 5, it is worth verifying.