In this work, blocks of magic rectangles with equal and unequal sums are used to construct magic squares. The equal sum blocks magic rectangles lead us to even order magic squares, such as, of orders 8, 12, 16, 20, 24, 28, 32, 36, 40, 42, 44 and 48. These magic squares are constructed using magic rectangles of orders 2x4, 2x14, 4x6, 6x10, 6x14, etc. There is only one example of even order magic square with different sums blocks of magic rectangles, i.e., of order 18. The odd order magic squares are with unequal sum blocks magic rectangles. These are of orders 15, 21, 27, 33, 39 and 45. These are constructed using magic rectangles of orders 3x5, 3x7, 3x9, 3x11, 3x13, 3x15, 5x7, etc. The magic squares of orders 12, 20, 24, 28, 42, 45 and 48 are written in two different ways. These magic squares are used to bring block bordered magic squares. These block bordered are of orders 10, 14, 17, 19, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46 and 47. Most of the magic squares from order 8 to 48 are studied in this work, except the orders 9, 11, 13 and 25. These are already studied by author in another work