Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 60

$\sum_{k=1}^{8} k^3$

We need to compute summation formula for the $1^3+2^3+3^3+.......+8^3$ We see that there are $8$ positive terms, take it as index $k$. When $k=1$, the first term is $1^3$ and for $k=2$ , the second term is $2^3$. Thus, we write the summation formula as follows: $1^3+2^3+3^3+.......+8^3= \sum_{k=1}^{8} k^3$