Not showing correct output for a input 100000 - Runtime error

Question

Sigma of Equation Given a number N, find the value of the below equation for the given number.

Equation

N
∑  {(X + 1)^2 - (3X + 1) + X}
X = 1

Input Format

First line contains an integer n

Output Format

Single line output representing the value.

Example 1

Input
1
Output
1

Example 2

Input
2
Output
5

Explanation

{(1+1)² - (3x1+1) + (1)} + {(2+1)² - (3x2+1) +2} = 4 - 4 +1 + 9 -7 +2 = 5

Constraints

1 <= n <= 105

**I have two solution one is working and second is not working for some test cases like n=100000.

Solution 1(Working):**

import java.util.*;
import static java.lang.Math.ceil;

class Solution {
    public long SigmaEquation(int n ) {
        long ans=0;
        for(int i=1; i<=n; i++){
            ans = ans + (long)(Math.pow((i+1),2)-((3*i)+1)+i);
        }
        return ans;
    }
}

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Solution Obj = new Solution();
        System.out.println(Obj.SigmaEquation(n));

    }
}

Solution 2(error for some test cases like n= 100000 ):-

import java.util.*;
import static java.lang.Math.ceil;

class Solution {
    public long SigmaEquation(int n ) {
        long ans=0;
        for(int i=1; i<=n; i++){
            ans = ans + (((i+1)*(i+1))-((3*i)+1)+i);
        }
        return ans;
    }
}

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Solution Obj = new Solution();
        System.out.println(Obj.SigmaEquation(n));

    }
}

Getting this issue for solution 2 why?

and why the same issue solved in solution 1 program?

Wrong Answer

Time Limit : 171ms
Time Taken By Your Code : 152ms

Input

100000

Correct Output

333338333350000

Your Output

18104913692784

Answer 1

(long)(Math.pow((i+1),2)-((3*i)+1)+i) from your first solution, you are casting the result of your equation as a long which supports very large numbers. in your second you are not casting to a long, so java assumes the result is an int. when the result of that equation starts to become very large, it no longer fits in an int so you are getting unexpected results from the later iterations of your for loop.