You can arrange a standard set of dominoes into a magic square of sorts. There are 28 dominoes, each with two ends, so the number of ends isn’t a perfect square. But if you ignore the row of blanks at the bottom, you have a 7 by 7 square where every row, column, and diagonal add to 24. (Technically this isn’t a magic square since some numbers repeat.)
If you don’t use all the dominoes you can make an actual square, no extra row to ignore:
While the most common set of dominoes goes up to double six, there are other possibilities. I made the images above by pulling out the double six subset out of a set of double nine dominoes. Is it possible to make magic squares like the first photo above out of a full set of dominoes up to double n for other values of n? Not if n is odd, but perhaps if n is even.
You can at least arrange the dominoes into a square. A set of double n dominoes has (n+1)(n + 2)/2 pieces, so (n+1)(n + 2) squares. With a row of n + 1 blanks on the bottom, this leaves (n + 1)2 squares in the magic square. The total number of points in a set of double n dominoes is n(n + 1)(n + 2)/2, so each row, column, and diagonal would have to sum to n(n + 2)/2. This means you cannot arrange a set of double n dominoes into a magic square if n is odd. So, for example, it won’t work for double nine dominoes. Is it possible when n is even? Certainly if n = 6, but what about other values of n?