Factors 3

$2016=2^5\times 3^2\times 7^1$
$6=2^1\times 3^1$
For those factors of $2016$ divisible by $6$ , they have the form
$2^a\times 3^b\times 7^c$ where $a=1,2,3,4,5$ ; $b=1,2$ ; $c=0,1$
The sum = $(2^1+2^2+\cdots 2^5)(3^1+3^2)(7^0+7^1)=62\times 12\times 8=5952$