Difference of Exponential Functions

Consider the exponential function defined by the equation:

$$ f(x) = 2^x $$

To find the value of $$ f(a + 3) $$, where $$ a $$ is an integer, calculate the difference between the outputs of this function at $$ a $$ and $$ a + 3 $$.

Determine the difference $$ f(a + 3) - f(a) $$ and express your answer in simplified form.