The smallest concentric magic square of even order is a 6x6 magic square consisting of a 4x4 magic square with a border around it. In a concentric magic square of odd order you find allways the middle number in the middle cell of the square. It is not possible to create a 4x4 magic square with the middle four numbers in the middle 2x2 cells. Closest to that is a symmetric 4x4 magic square, for example the Dürer magic square (see famous magic squares). 

Add 10 to all numbers of the 4x4 magic square and construct a 6x6 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 concentric magic square. Add 14 to all numbers of the 4x4 in 6x6 magic square and construct a 8x8 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 in 8x8 concentric magic square. You can put borders around it to infinite.

Remove the border of a 4x4 in 6x6 in 8x8 in 10x10 concentric magic square and you get an (impure) 8x8 magic square. Remove the border and you get a 6x6 magic square. Remove the border and you get a 4x4 magic square.

See how the concentric magic square on this website is growing bigger and bigger: 

3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9x9, 10x10, 11x11, 12x12, 13x13, 14x14, 15x15, 16x16, 17x1718x18, 19x19, 20x20, 21x21, 22x22, 23x23, 24x24, 25x25, 26x26, 27x27, 28x28, 29x29,  30x30, 31x31 and 32x32