Explanation 7x7 magic square
Magic square of order 7 is odd and a prime number, just like the magic square of order 5, so you can use the same construction methods.
For more detailed explanation see the 5x5 magic square.
The construction methods of the 7x7 magic square are:
With the first five methods you get simple, symmetric 7x7 magic squares.
With the shift method you can construct all panmagic 7x7 squares.
Most perfect magic 7x7 square is panmagic and symmetric (= ultra magic).
It is also possible to construct a (pure) 7x7 magic square with a 5x5 inlay magic square or a 3x3 in 5x5 in 7x7 (concentric) magic square.