$$\sigma_3 = \sum_{k=0}^7 (k+2)^3 $$
in the image I have attached you can see an equation which I can not solve. However one student at my university who has solved the equation has added an 8 (+8) to the equation in the next step and has increased the "0" under the summation sign to a 1. I think if you could explain why he/she did that it would be a great help. Thanks.
$\sum_{k=0}^{7}(k+2)^3=\sum_{k=0}^{7}(k^3+6k^2+12k+8)= \sum_{k=0}^{7} k^3+6\sum_{k=0}^{7}k^2+12\sum_{k=0}^{7}k+\sum_{k=0}^{7}8$.
$k=0$ doesn't contribute in the first 3 terms, but you must count it in the final as it doesn't depend on $k$.