Let f be a real valued continuous function defined on the positive real axis such that g (x)=∫_0^x t f( t ) dt. If g (x^3)=x^6+x^7, then value of…

Let $\displaystyle f$ be a real valued continuous function defined on the positive real axis such that $\displaystyle \mathrm{g}(x)=\int_0^x \mathrm{t} f(\mathrm{t}) \mathrm{dt}$. If $\displaystyle \mathrm{g}\left(x^3\right)=x^6+x^7$, then value of $\displaystyle \sum_{r=1}^{15} f\left(\mathrm{r}^3\right)$ is :