Let \(f\) be a real valued continuous function defined on the positive real axis such that \(g(x)=\int_0^x t f(t) d t\) …

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

[JEE Main 2025, 28 Jan (Shift 2)]