Sums of Squares in Lines of Order 3 Magic Square

Theorem
Consider the order 3 magic square:


 * The sums of the squares of the top and bottom rows are equal, and differ by $18$ from the sums of the squares of the middle row
 * The sums of the squares of the left and right columns are equal, and differ by $18$ from the sums of the squares of the middle column.

Proof
For the rows:

For the colums: