The sum to infinity of the series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots$ is

Statement 1: The sum of the series $1+\left(1+2+4\right)+\left(4+6+9\right)+\left(9+12+16\right)+...+\left(361+380+400\right)$is $8000.$

Statement 2: $\sum _{k=1}^n\left(k^3-{\left(k-1\right)}^3\right)=n^3,$ for any natural number $n.$