Find the sum of the series up to $10$ terms: $(3^3 - 2^3) + (5^3 - 4^3) + (7^3 - 6^3) + \dots$

For all $n \in N$,if $1^3+2^3+3^3+\ldots+n^3 > x$,then a value of $x$ among the following is

Let $f(n) = \left[ \frac{1}{3} + \frac{3n}{100} \right]n$,where $[x]$ denotes the greatest integer less than or equal to $x$. Then $\sum_{n=1}^{56} f(n)$ is equal to

For a series $S = 1 - 2 + 3 - 4 + \dots$ up to $n$ terms,
Statement-$1$: The sum of the series is always dependent on the value of $n$,i.e.,whether it is even or odd.
Statement-$2$: The sum of the series is $-\frac{n}{2}$ when the value of $n$ is any even integer.

The value of $\sum\limits_{n = 0}^\infty {\frac{{{{(n + 1)}^2}}}{{{7^n}}}}$ is -

The odd numbers are divided as follows:
Row $1$: $1, 3$
Row $2$: $5, 7, 9, 11$
Row $3$: $13, 15, 17, 19, 21, 23$
Then the sum of the $n^{th}$ row is: