  We study the divisibility of the sums of the odd power of consecutive
integers, $S(m,k)=1^{mk}+2^{mk}+\cdots+k^{mk}$ and $1^k+2^k+\cdots+n^k$ for odd
integers $m$ and $k$, by using the Girard-Waring identity. Faulhaber's approach
for the divisibilities is discussed. Some expressions of power sums in terms of
Stirling numbers of the second kind are represented.
