For the first time in this work, two new concepts in construction of magic square are considered:

Using small blocks of magic or bordered magic rectangles. It is not always possible to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered.

Using algebraic formula (a+b)^{2}.

The whole work contains magic squares of even orders starting from order 8. This part is only for order 8 and 10. For orders 12, 14 and 16 see the links below:

Inder J. Taneja, Different Styles of Magic Squares of Orders 8, 10 and 12 Using Bordered Magic Rectangles and the Formula (a+b)^{2}, Zenodo, September 18, 2022, pp. 1-30, https://doi.org/10.5281/zenodo.7090737.

Inder J. Taneja, Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles and the Formula (a+b)^{2}, Zenodo, September 18, 2022, pp. 1-45, https://doi.org/10.5281/zenodo.7090764.

Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles and the Formula (a+b)^{2}, Zenodo, September 18, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7090770.

Below are a few Examples of Magic Squares of order 8 and 10. These are written in four parts:

Part 1: Magic Squares of Order 8;

Part 2: Magic Squares of Order 10;

Part 3: Magic Squares of Order 10: (A+B)^{2}-Type: A=6, B =4;

Part 4: Bordered and Block-Bordered Magic Squares of Order 10.

Part 1: Magic Squares of Order 8

Part 2: Magic Squares of Order 10

Part 3: Magic Squares of Order 10: (A+B)^{2}-Type, A=6, B=4

Part 4: Bordered and Block-Bordered Magic Squares of Order 10