Calculate Squares of a Grid

In Mathematics, we are have been working on how to calculate the numbers of squares outside the  10x10 grid. We have found out that there are 6 ways of doing it.

This what I found out:

My theory for working out the number of squares in a border is counting the outsides of the grids and since there are 4 sides and the grids are 10by10 you have to multiply the 10 by 4 so its 4x10 and the answer will be 40 and since you count the corner twice you have to take away 4 and the answer will 36

Methods:
10+10+10+10 - 4 = 36
(4x10)-4 = 36
Algebra: N(n) = 10
(n+n+n+n-4)
(4n - 4) = (answer)

Other Methods:
The other theory for working out the number of squares in a border is multiplying the outside of the grids which is the 10x10 and the answer will be 100 and the inside squares will be 8x8 and the answer will be 64 and once you get both answers you subtract them together(100-64) and the answer will be 36.

Methods: 100 - 64 = 36

10x10 =100

8x8 = 64

Algebra: N(n) = 10

(n x n = 100)

( n-2 x n-2 =64)

There also other methods or formula on how to calculate. First, you have to count the top which is 10 and count the 2 sides of the outside grids which are 9, it's 9 because we already count the top and we are not gonna count it again and the bottom grids will be 8 because of we already count the sides.
In this method you have to do is 10 + 9 + 9 + 8 = 36.

Example:

10+9+9+8 = 36

Algebra:

(n + n-1 + n-1 + n-2 = 36)

n + 2(n-1) + n-2 = 36

Proof of 6 ways of doing it.

Did you understand the example?