3. (7 points) Calculate the sum

$$
1 \cdot 2+2 \cdot 3+3 \cdot 4+\ldots+2015 \cdot 2016
$$

Answer: 2731179360
Solution. Notice that $1 \cdot 2+2 \cdot 3+3 \cdot 4+\ldots+n \cdot(n+1)=\frac{n \cdot(n+1) \cdot(n+2)}{3}$.