Points on the x-axis $-R,\cdots,-\frac{R}{n},0,\frac{R}{n},\frac{2R}{n},\cdots,\frac{(n-1)R}{n},R$. Point $M(R\cos \alpha,R\sin \alpha)$. Sum $=\sum_{k=1}^{k=n}[(R\cos \alpha+\frac{k \cdot R}{n})^{2}+(R\cos \alpha)^{2}] + R^{2}+ \sum_{k=1}^{k=n}[(R\cos \alpha-\frac{k \cdot R}{n})^{2}+(R\cos \alpha)^{2}]$. Sum $=\sum_{k=1}^{k=n}(2R^{2}+2\frac{k^{2} \cdot R^{2}}{n^{2}}) + R^{2}$. Sum $=2nR^{2}+2 \cdot \frac{1}{6}n(n+1)(2n+1) \cdot \frac{R^{2}}{n^{2}} + R^{2}=\frac{(2n+1)(4n+1)}{3n} \cdot R^{2}$.