For the most part, you do not need a Commercial Drivers License to drive a box truck. The parameters for whether or not you need a CDL to drive a box truck are the following:
If the Gross Vehicle Weight Rating (GVWR) is 26,001 pounds or above, you need a commercial driver's license (CDL) to operate it.
If the GVWR is 26,000 pounds or below, you do not need a CDL license.