The sum of the squares of the first ten natural numbers is,

`1^2 + 2^2 + ... + 10^2 = 385`

The square of the sum of the first ten natural numbers is,

`(1 + 2 + ... + 10)^2 = 552 = 3025`

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is

`3025 − 385 = 2640`

.Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

At first the `$sum_of_squares`

and `$sums`

are equal to `1`

.

After calculating the hardest part (`calculating 1`

) without using programming we are ready to start out `for`

loop from `2`

and add the second powers of the `$number`

s to `$sum_of_squares`

by also adding the `$number`

to `$sums`

each time.

```
$sum_of_squares = $sums = 1;
for ($number = 2; $number <= 100; $number++)
{
$sum_of_squares += ($number * $number);
$sums += $number;
}
$result = ($sums * $sums) - $sum_of_squares;
```

At last we will need to get the second power of `$sums`

and subtract `$sum_of_squares`

from it.

**Execution time: 0s**