Editing Centered cube number (section)

==Formulas==
The centered cube number for a pattern with {{mvar|n}} concentric layers around the central point is given by the formula<ref>{{citation|title=Figurate Numbers|first1=Elena|last1=Deza|author1-link=Elena Deza|first2=Michel|last2=Deza|author2-link=Michel Deza|publisher=World Scientific|year=2012|isbn=9789814355483|pages=121–123|url=https://books.google.com/books?id=cDxYdstLPz4C&pg=PA121}}</ref>

:<math>n^3 + (n + 1)^3 = (2n+1)\left(n^2+n+1\right).</math>

The same number can also be expressed as a [[trapezoidal number]] (difference of two [[triangular number]]s), or a sum of consecutive numbers, as<ref>{{citation|title=Concepts in Abstract Algebra|first=Charles|last=Lanski|publisher=American Mathematical Society|year=2005|isbn=9780821874288|page=22|url=https://books.google.com/books?id=X1ttNRvbNK0C&pg=PA22}}.</ref>
:<math>\binom{(n+1)^2+1}{2}-\binom{n^2+1}{2} = (n^2+1)+(n^2+2)+\cdots+(n+1)^2.</math>