is there any size $N\cdot N$Sudoku Puzzle where the smaller $\sqrt N\cdot\sqrt N$ squares all form magic squares

Question

Any $N\cdot N$ Sudoku Puzzle has $N$ squares size $\sqrt N\cdot\sqrt N$ that each have the numbers $1$ to $N$ in them.Is there a sudoku puzzle of any size that have magic squares for all of these sub-squares? I think it will be inevitable for large enough $N$, since there will be more possible Sudokus.

Answer 1

Yes, there is a solution for $16\cdot16$: