Here's my math, & I think it is right:
Volume = pi * r^2 * d
= 3.14 * 15^2 * 7 = 4945 cu in
This is approx 21 US gal (231 cu in per gal).
Sudz - your metric conversion is wrong. There is 16.4 ml per cu in, not 2.2
DocOc - you use pi * d for area, which is the diameter equation, not area equation
However, a finished "cookie" fitting into the space will not hold the 21 gal of water. The biggest limitation is that you cannot fill such a tank to the top. The amount you can fill will be determined by the surface area of the water. If the cookie is filled to the brim, there will be zero suface area for gas exchange & your fish will die .... (This is the same reason not to fill a goldfish bowl to the brim ... ) Maximum surface area will be when the tank is half full .... You may be able to push 2/3 full (That would be roughly half the SA of half full, & approx 100 sq inches of SA). For comparasion, a standard 10 gal tank has a SA of 150 Sq in. So even though the cookie has more water than 10 gal, you really should stock it as if it is a 10 gal due to SA limitations.
To make a long story short - The most you can get in a setup like that is 15 gal or so. Plus you will have a water line somewhere in the middle of the circle .... prob not what you are imagining.
I would think that building a rectangular tank bigger than the circle opening & fitting that inside the wall would be the best - both in terms of estetics & tank volume, SA & maintanance issues. That, however, would mean tearing open the wall for installation & making some access panel for maintanance.