Let X=$\frac{n(5n+1)(10n+1)}{6}$
For n=1 X= $\frac{6*11}{6}=11$
For n=2 X=$\frac{2*11*21}{6}=77$
For n=3 X=$\frac{3*16*31}{6}=248$
For n=4 X=$\frac{4*21*41}{6}=574$
Here we can see X is not divisible 3 and 5 but X is always an Integer.
Hence,Option(C)Is always an integer.