In the first line we have nnn which has been replace by n*(n-1)(n-2)
This is valid because we are saying that that S^3 is greater or equal to the first line and since nnn > n(n-1)*(n-2) for all n, it is a valid substitution.
The next 3 terms are (n-3)(n-3)(n-3) which is then replaced by (n-3)(n-4)(n-5). This is valid because (n-3)(n-3)(n-3)>(n-3)(n-4)(n-5) for all n.
The factors continue repeating 3 numbers and being replaced by 3 consecutive decreasing numbers. The new group of numbers is always less than the 3 numbers it replaced so the new group of numbers is always a valid substitution.
The advantage of these substitutions is that you can combine the numbers to equal n!