Answer
$1^{3}+2^{3}+3^{3}+\displaystyle \cdots+8^{3}=\sum_{k=1}^{8}k^{3}$
Work Step by Step
$1^{3}+2^{3}+3^{3}+\cdots+8^{3}=$
There are 8 terms, count them with index k: $\displaystyle \sum_{k=1}^{8}$(...)
The first term (when k=1) is $1^{3}$,
The second term (when k=2) is $2^{3}$,
The kth is $k^{3}$ so
$1^{3}+2^{3}+3^{3}+\displaystyle \cdots+8^{3}=\sum_{k=1}^{8}k^{3}$