This constant sum, the so-called magic sum is given by
This means that n2 numbers are placed in a grid with n rows and n columns. There is a wellknown formula for the sum of first n consecutive numbers:
If we now add up to n2, this formula will change to
With this result it is easy to calculate the magic sum
The following table shows some magic sums:
For a magic square of order n=8 we will get therefore M(8)=260.