CompositeSquares makes these squares.
A composite square of order MN, (M times N), can be made from a square of order M and a square of order N. It contains N² order M magic squares using the numbers 1 to (MN)² The smallest are order-9 from order-3 and order-3. They are made up of 9 order-3 magic squares using the numbers 1 to 81.
The next are order-12, consisting of 16 order-3 or 9 order-4 magic squares, using the numbers 1 to 144.
Different aspects of the same squares make distinct composite squares. For example, 8 distinct order-9 magic squares can be made from the 8 aspects of the Lo Shu:
Some properties of the order M and order N squares are preserved in the composite square. If the order M square and the order N square are both associative, the composite square is associative. The 3-3Composites and the 4-3Composite above are associative.
The pandiagonal and self-complement properties are also preserved in composite squares.
Heinz, Harvey "Composition Magic Square" http://www.magic-squares.net/glossary.htm
Rouse Ball, W.W. "Other Methods For Constructing Any Magic Square"
http://www.gutenberg.org/files/26839/26839-pdf.pdf, page 134.