PHP program to find the sum of cubes of the first n natural numbers

To find the sum of cubes of the first n natural numbers, we can use a loop to iterate through each number and calculate its cube. The formula for the cube of a number is n³ = n × n × n.

Example

Here's a PHP program that calculates the sum of cubes for the first n natural numbers ?

<?php
function sum_of_cubes($val)
{
    $init_sum = 0;
    for ($x = 1; $x <= $val; $x++)
        $init_sum += $x * $x * $x;
    return $init_sum;
}
print_r("The sum of cubes of first 8 natural numbers is ");
echo sum_of_cubes(8);
?>

Output

The sum of cubes of first 8 natural numbers is 1296

How It Works

The sum_of_cubes() function takes a parameter $val representing the number of natural numbers to process. It initializes $init_sum to 0, then uses a for loop to iterate from 1 to $val. For each number $x, it calculates the cube ($x * $x * $x) and adds it to the running sum.

Alternative Method Using Formula

There's also a mathematical formula: sum of cubes of first n natural numbers = [n(n+1)/2]² ?

<?php
function sum_of_cubes_formula($n)
{
    $sum = ($n * ($n + 1) / 2);
    return $sum * $sum;
}
echo "Using formula: " . sum_of_cubes_formula(8);
?>

Using formula: 1296

Conclusion

Both methods produce the same result, but the formula approach is more efficient for large values of n as it runs in constant time O(1) instead of O(n).