It is always possible to block-wise magic squares of any order except for the orders of type p and 2p, where p is a prime number. On the other hand, one can always write bordered magic squares of any order. In the previous works, the author combined the both, i.e., bordered and block-wise magic squares, calling block-bordred magic squares. See the following links:

This work brings block-wise bordered and block-wise block-bordered magic square. The bordered and block-bordered magic squares are written as sub-blocks of equal or different sums. The magic squares studied are of orders 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42 and 44. The work is with even order multiples, i.e, multiples of orders 6, 8, 10, 12, 14, 16, 18 and 22. The work can be downloaded at the following link:

Inder J. Taneja, Bordered and Block-Wise Bordered Magic Squares: Even Order Multiples, Zenodo, February 10, 2021, pp. 1-96, http://doi.org/10.5281/zenodo.4527746

Below are examples of magic squares studied in the work. In all the cases blocks considered are of equal sums except, where we have blocks of order 3 and 5. For odd order multiples see the another link:

Examples:

Block-Wise Bordered Magic Square of Order 12

Block-Bordered and Block-Wise Bordered Magic Square of Order 16

Block-Wise Bordered Magic Square of Order 18

Block-Bordered and Block-Wise Bordered Magic Square of Order 20

Block-Bordered and Block-Wise Bordered Magic Squares of Order 24

Block-Bordered and Block-Wise Bordered Magic Squares of Order 28

Block-Bordered and Block-Wise Bordered Magic Squares of Order 30

Block-Bordered and Block-Wise Bordered Magic Squares of Order 32

Block-Bordered and Block-Wise Bordered Magic Squares of Order 36

Block-Bordered and Block-Wise Bordered Magic Squares of Order 40

Block-Bordered and Block-Wise Bordered Magic Squares of Order 42

Block-Bordered and Block-Wise Bordered Magic Squares of Order 44

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