Find the sum of $n$ terms of the series $1·3·2^2+2·4·3^2+3·5·4^2+\dots \dots$

Find the sum of $n$ terms of the series $\left(n^2-1^2\right)+2\left(n^2-2^2\right)+3\left(n^2-3^2\right)+\dots \dots$

Find the sum of $n$ terms of the series whose nth terms is $n^2\left(n^2-1\right)$.

Find the sum of $n$ terms of the series whose $n$th term is $\left(n^2+5n+4\right)\left(n^2+5n+8\right)$

Find the sum of $n$ terms of the series, whose $n^{\text{th}}$ term is $\frac{n^2\left(n^2-1\right)}{4n^2-1}$

Find the sum of $n$ terms of the series, whose $n^{\mathrm{th}}$ term is $\frac{n^4+2n^3+n^2-1}{n^2+n}$

Find the sum of $n$ terms of the series whose  $n\mathrm{th}$ term is

$\frac{n^3+3n^2+2n+2}{n^2+2n}$

Find the sum of $n$ terms of the series whose  $n^{\text{th}}$ term is $\frac{n^4+n^2+1}{n^4+n}$