What is the square of $21$?

Look at this method:

$2^2=1^2+\left(1+2\right)$

$3^2=2^2+\left(2+3\right)$

Using the above method, find the square of $51$.

Look at this method:

$2^2=1^2+\left(1+2\right)$

$3^2=2^2+\left(2+3\right)$

Using the above method, find the square of $61$.

Look at this method:

$2^2=1^2+\left(1+2\right)$

$3^2=2^2+\left(2+3\right)$

Using the above method, find the square of $121$.

Look at this method:

$2^2=1^2+\left(1+2\right)$

$3^2=2^2+\left(2+3\right)$

Using the above method, find the square of $1001$.

Look at this method:

$2^2=1^2+\left(1+2\right)$

$3^2=2^2+\left(2+3\right)$

Using the above method, compute the squares of natural numbers from $90$ to $100$.

What is the relation between the difference of the squares of alternative natural numbers and their sum?