Statement 1 The sum of the series \[ \begin{aligned} 1+(1+2+4)+(4+6...

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Statement 1 The sum of the series
\[
\begin{aligned}
1+(1+2+4)+(4+6+9)+(9+12+16) \\
+\ldots+(361+380+400) \text { is } 8000 .
\end{aligned}
\]
Statement \( 2 \sum_{k=1}^{n}\left(k^{3}-(k-1)^{3}\right)=n^{3} \) for any natural number \( n \).
[AIEEE 2012, 4M]
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(c) Statement-1 is true, Statement-2 is false
(d) Statement-1 is false, Statement-2 is true
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