437. What sequence do the differences between the differences («second differences») of the cubes of consecutive natural numbers form?
437. The first differences of the cubes of consecutive natural numbers are given by the formula: $(n+1)^{3}-n^{3}=3 n^{2}+3 n+1$. The second differences are obtained by the formula: $\left[3(\boldsymbol{n}+1)^{2}+3(\boldsymbol{n}+1)+1\right]$ $\left[3 n^{2}+3 n+1\right]=6 n+6$; this expression is the $n$-th term of an arithmetic progression, the first term of which is 12, and the common difference is 6.