Octahedral number

Statement

The $n$-th octahedral number is $\mathrm{Oct}_n=\dfrac{n\,(2n^2+1)}{3}$. Compute $\mathrm{Oct}_6$.

Solution

$\mathrm{Oct}_6=\frac{6\,(2\cdot 36+1)}{3}=\frac{6\cdot 73}{3}=2\cdot 73=\boxed{146}.$