# Java Program - Calculate sum of Cubes of Natural numbers

In Mathematics, the natural numbers are all positive numbers which is used for counting like 1, 2, 3, 4, and so on. The smallest natural number is 1.

Objective: Write a Java program which returns sum of cubes of natural numbers starting from 1 to given natural number n, (13 + 23 + 33 + ... + n3).

### Method 1: Using while loop

The example below shows how to use while loop to calculate sum of cubes of first n natural numbers.

```public class MyClass {
public static void main(String[] args) {
int n = 10;
int i = 1;
int sum = 0;

//calculating sum of cubes from 1 to n
while(i <= n) {
sum += i*i*i;
i++;
}

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 3025
```

### Method 2: Using for loop

The same can be achieved using for loop. Consider the example below:

```public class MyClass {
public static void main(String[] args) {
int n = 10;
int sum = 0;

//calculating sum of cubes from 1 to n
for(int i = 1; i <= n; i++)
sum += i*i*i;

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 3025
```

### Method 3: Using Recursion

Similarly, recursion can be used to calculate the sum.

```public class MyClass {
//recursive method
static int Sum(int n) {
if(n == 1)
return 1;
else
return (n*n*n + Sum(n-1));
}

public static void main(String[] args) {
System.out.println("Sum of Cubes of first 10 natural numbers: " + Sum(10));
System.out.println("Sum of Cubes of first 20 natural numbers: " + Sum(20));
}
}
```

The above code will give the following output:

```Sum of Cubes of first 10 natural numbers: 3025
Sum of Cubes of first 20 natural numbers: 44100
```

### Method 4: Using Mathematical Formula

The sum of cubes of first n natural numbers can be mathematically expressed as: ```public class MyClass {
public static void main(String[] args) {
int n = 10;

//calculating sum of cubes from 1 to n
int sum = n*(n+1)/2;
sum *= sum;

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 3025
```

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