The idea of **nested magic squares** is well known in the literature, generally known by** bordered magic squares**. Instead, considering entries as consecutive numbers, we considered **consecutive odd numbers entries**. This gives us **perfect square sum magic squares**. We worked with magic squares of orders 3 to 25. Finally, the result can be written in a symmetric way, i.e.,

T_{m x k}:= m^2 x k^2,

where * m* is the order of

**nested magic square**,

*is the order of*

**k****sub-magic squares**in each case, and

*is the total entries sum. Also the entries sums are connected with*

**T****Pythagorean triples**and borders. In each case, the

**difference among consecutive borders sums**is always a fixed value. Below is link for download the work and some examples:

- I.J. Taneja, Nested Magic Squares With Perfect Square Sums, Pythagorean Triples, and Borders Differences, June 14, 2019, pp. 1-59, http://doi.org/10.5281/zenodo.3246586.

**Link for download the work:**

- I.J. Taneja, Nested Magic Squares With Perfect Square Sums, Pythagorean Triples, and Borders Differences, June 14, 2019, pp. 1-59, http://doi.org/10.5281/zenodo.3246586.