Only a few algorithms are known which could construct magic squares of any even order (n=4,6,8,...). Usually most of the algorithms use the symmetry of double-even and the asymmetry of the single-even squares, so that these methods will only work for a special group of magic squares.
But there are also some algorithms to create magic squares for all even orders. The most famous algorithm is related to Devedec, who found a rather complicated pattern. The second algorithm was published as a computer program. The author of the program mentioned that he found this algorithm somewhere, but didn't cite the original author.
All algorithms are described in detail in my PDF book. (chapter: Magic Squares of even order)