The smallest odd inlay square is a (not pure) 3x3 magic square inside a (pure) 5x5 magic square. It is possible to use the consecutive middle 9 numbers from 1 up to 25 to construct the inlay. Use the 8 highest numbers and the 8 lowest numbers to construct the border. See the result below:
Number + 8 = add border = 3x3 in 5x5 magic square
22 | 18 | 3 | 2 | 20 | ||||||||||
2 | 9 | 4 | 10 | 17 | 12 | 7 | 10 | 17 | 12 | 19 | ||||
7 | 5 | 3 | 15 | 13 | 11 | 5 | 15 | 13 | 11 | 21 | ||||
6 | 1 | 8 | 14 | 9 | 16 | 25 | 14 | 9 | 16 | 1 | ||||
6 | 8 | 23 | 24 | 4 |