An arithmetic sequence is of the form a, a+d, a+2d,..., a+(n-1)d.
This produces the sum na+d(1+2+..+n-1)=na+nd(n-1)/2=½(2a+nd-d)n.
This expression is a quadratic in n, so there is n no cube term, and 9-n³ could not be the sum to n terms of any arithmetic sequence.
However, if 9-n³ defines the nth term of a series (non-arithmetic), then we can calculate each term from 2 to 7:
1, -18, -55, -116, -207, -334, the sum of which is -729.