But 2016 isn't here yet!

Algebra Level 3

Evaluate the expression $\large {\frac{2016^{4}+2016^{2}+1}{2016^{3}+1}}$ .

If the answer can be expressed as a mixed fraction in simplest form $a \frac{b}{c}$ , find $a+b+c.$

Note: Solve this problem without using a calculator.