The smallest ball permitted by USGA rules is 1.68 inches in diameter, which would yield a minimum volume of about 2.48 cubic inches (40.68 cm3) -- the dimples vary in number and depth, so the displaced volume would be slightly smaller. Historically, there was a smaller "British" ball that yielded some advantage in distance.
How to compute
V = 4/3 (pi) r3 (4 x 3.1416 x radius cubed)
How to measure
The easiest way to check would be to put a Golf ball in a beaker of water. Fill a 200 ml beaker with water, and place the ball in. Catch the overflow in another measured beaker. Since water is almost exactly 1 ml = 1 cc, the liquid displaced by the completely submerged ball will provide a close estimate of its volume in cm3.
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