This document presents two new general methods for constructing doubly even magic squares of any order. It shows that these methods naturally generate Durer's magic square when the order is 4. The methods are demonstrated through examples of order 4 and 8 magic squares. While the order 8 square is magic, squares of order n will only be magic if n is not a multiple of 8. The results allow defining generalizations of Durer's magic square for orders greater than 4.