  This paper proposes an elementary solution to a special case of finding all
perfect squares that can be written as sum of consecutive integer cubes. It is
shown that there are no non-trivial solutions if the perfect square is a prime
power, i.e., it is divisible by two different primes if a non-trivial one
exists. Solution mostly depends on $v_{p}(x)$ and general forms of Pythagorean
triples.
