Volume of a Region Surrounding a Cube

A cube-shaped satellite has edge length $ 10 $ meters. Let $ S $ be the set of all points outside the satellite such that each point in $ S $ is at most $ 3 $ meters away from the point in the surface of the satellite closest to it. How many cubic meters is the volume of $ S $? The answer is in the form $\alpha + \beta \pi$ where $\alpha$ and $\beta$ are positive integers. Input the value of $\alpha + \beta$.