Let \( f \) be a real valued continuous function defined on the positive real axis such that \(\displaystyle g(x) = \int_{0}^{x} t\, f(t)\, dt \). If \( g(x^{3}) = x^{6} + x^{7} \), then value of \(\displaystyle \sum_{r=1}^{15} f(r^{3}) \) is:
\( 340 \)
\( 320 \)
\( 310 \)
\( 270 \)
