What is the value of a 30-06 Belgian Browning Model 710721 rifle with the box in mint condition and never fired?
That is not a valid Browning model designation.
Do browning shotguns made in the US have any special value considering the fact that they were not made in belgium and also the fact that not very many were manfactured due to the war?
No, the value of American made Browning Auto-5's, are less than the Belgian models based on like condition. The American made models were made using Remington model 11 machinery. While tens of thousand American models were made during the war, few Belgian models were made and/or assembled during that time. There are very few collectors that are interested in American made Brownings versus the Belgian Browning Collectors.
Browning Superposed Shotgun is what you have Superposed shotguns are very collectable when in top condition. Values have a wide range due to so many variations and grades of the Superposed and other Browning Over/Unders. Value is too difficult to be accurate without seeing the gun. Condition which includes the amount of original finish and original configuration will determine value. Recommend taking it to a gun shop for appraisal.