To calculate the sum of the digits of a number in base 10 using Mathematica, the correct command is to use `Plus @@ IntegerDigits[number]`. For example, to find the sum of the digits of 380234, you would input `Plus @@ IntegerDigits[380234]`, which outputs 20. The discussion highlights that defining a function like `s[3^14, 10] := Plus @@ IntegerDigits[3^14, 10]` is unnecessary for a quick calculation, as it requires evaluation after definition. Instead, directly inputting the command without defining a function yields immediate results.