The author worked on different kinds of magic squares. These include block-wise, bordered, block-bordered and block-wise bordered magic squares. The block-wise bordered magic squares are very much similar to bordered magic squares, where the numbers are replaced by blocks of magic squares. For the first time in recent works (paper1, paper2, paper3, paper4), the author considered two new concepts in construction of magic squares. The first one is by using small blocks of magic or bordered magic rectangles. It is not possible always to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered. The second aspect is based on the algebraic formula (a+b)^2. The work is still limited to even order magic squares. It is done for the magic squares of orders 8, 10, 12, 14, 16 and 18. This brings few examples of similar type for the orders 20, 22, 24, 26, 28 and 30. The extended study shall be given elsewhere.