When n is a natural number, it is assumed that a number in the form of 2(2n+ 1) can be expressed as the square difference of two integers. Let two integers be A, B, a>b.

2*(2n+ 1)=a^2-b^2=(a+b)(a-b)

Obviously, a+b and a-b have the same parity.

The left is even, so (a+b)(a-b) is even.

Therefore, a+b and a-b are even numbers, and the right side of the equation can be divisible by 4, but the left side of the equation cannot be divisible by 4, which is contradictory.

So 2*(2n+ 1) cannot be expressed as the square difference of two integers.