Finding Method C

Below is a 6*6 matrix displayed in Shanxi Museum in Xi'An:

It was explained that's to do with an custom of architecture in ancient China: it was berried for good fortune under the ground of a new building to be built, because, the sum of the 6 numbers in every row, every column and diagonal, is the same of 111 - lucky numbers of 6 lead to another lucky number 111. The distribution of the 36 numbers seem in random like the raw materials of a building - so how to fill them in turn to "build up" such a "lucky" square?

Mr. Chen Shu Jie, my respected old classmate, told me that this is the mathematic game of filling numbers from 1 to n² into the n*n square matrix and reach the magic result: the sum in row, column and diagonal is the same of (n³+n)/2. Above, n=6, so the sum is (6³+6)/2=111.

He further explained that there are two methods he has known to fill the numbers, which are depending on whether n is an odd or even number.

If it is an odd number, n=3, for example, below is the 3*3 magic square:

Method A:
Firstly fill "1" into the middle grid of the last row, then fill "2" into the grid of "row+1" and "column+ 1", if the grid is occupied, then go to another grid of "row-1" in the same column.
Same for a 5*5 magic square:

If it's an even number, provided n=4, below is his answer:

Method B:
Firstly, fill the numbers from 1 to 16 in turn from left to right, row by row, then exchange every two numbers on the opposite grids on the diagonal, i.e, 1 and 16, 4 and 13, 6 and 11 etc.
So here is a 6x6 square accordingly:

Then by rotating or reflecting, we know other relative squares.
Now, the problem is: How was the 6*6 Matrix in Shanxi Museum made? There must exist another method? - so what is the method C??