Hi,
A)
[tex] \dfrac{n(2n+1)(7n+1)}{6} \\
= \dfrac{14n^3+9n^2+n}{6} \\
= \dfrac{12n^3+6n^2}{6} + \dfrac{2n^3+3n^2+n}{6} \\
=2n^3+n^2+ \dfrac{n(2n^2+3n+1)}{6} \\
= 2n^3+n^2+ \dfrac{n(n+1)(2n+1)}{6} \\
= 2n^3+n^2+ 1^2+2^2+3^2+...+n^2\ is\ an\ integer.
[/tex]
B)
Only if n=4*k or n=4*k+1 , k beeing an integer.
