The lowly 3×3 magic square has modest pretensions — each row, column, and diagonal produces the same sum.

But perhaps it’s magicker than we suppose:

618² + 753² + 294² = 816² + 357² + 492² (rows)
672² + 159² + 834² = 276² + 951² + 438² (columns)
654² + 132² + 879² = 456² + 231² + 978² (diagonals)
639² + 174² + 852² = 936² + 471² + 258² (counter-diagonals)
654² + 798² + 213² = 456² + 897² + 312² (diagonals)
693² + 714² + 258² = 396² + 417² + 852² (counter-diagonals)

(R. Holmes, “The Magic Magic Square,” The Mathematical Gazette, December 1970)

More: Any of the equations above will still hold if you remove the middle digit or any two corresponding digits in each of the six addends.

Yet more: (6 × 1 × 8) + (7 × 5 × 3) + (2 × 9 × 4) = (6 × 7 × 2) + (1 × 5 × 9) + (8 × 3 × 4)

I think everything above will work for any rotation or reflection of the square (that is, for any normal 3×3 magic square). I haven’t checked, though.