amc-2014-im-29

As shown in the diagram, you can create a grid of squares 3 units high and 4 units wide using 31 matches.

I would like to make a grid of squares \(a\) units high and \(b\) units wide, where \(a<b %speech% ,a less than b,\) are positive integers.

Determine the sum of the areas of all such rectangles that can be made, each using exactly 337 matches.