  We study the equation $(x-4r)^3 + (x-3r)^3 + (x-2r)^3+(x-r)^3 + x^3 +
(x+r)^3+(x+2r)^3 + (x+3r)^3 + (x+4r)^3 = y^p$, which is a natural continuation
of previous works carried out by A. Arg\'{a}ez-Garc\'{i}a and the fourth author
(perfect powers that are sums of cubes of a three, five and seven term
arithmetic progression). Under the assumptions $0 < r \leq 10^6$, $p \geq 5 $ a
prime and $\gcd(x, r) = 1$, we show that solutions must satisfy $xy=0$.
Moreover, we study the equation for prime exponents $2$ and $3$ in greater
detail. Under the assumptions $r>0$ a positive integer and $\gcd(x, r) = 1$ we
show that there are infinitely many solutions for $p=2$ and $p=3$ via explicit
constructions using integral points on elliptic curves. We use an amalgamation
of methods in computational and algebraic number theory to overcome the
increased computational challenge. Most notable is a significant computational
efficiency obtained through appealing to Bilu, Hanrot and Voutier's Primitive
Divisor Theorem and the method of Chabauty, as well as employing a Thue
equation solver earlier on.
