Factorials expressed as sum and difference of squares

The factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.

http://en.wikipedia.org/wiki/Factorial

http://mathworld.wolfram.com/Factorial.html

To show that

(1) it is possible to express n! as the difference of two perfect squares for all positive integers except n = 2 and n = 3, that is

n! = a^2 - b^2

(2) whether it is possible to express n! as the sum of two squares, that is

n! = a^2 + b^2

See sequence A138196 http://oeis.org/A138196