Finally it got solved. take a look.
public class Solution {
    static int mod = 1000000007;
    static int summingSeries(long n) { 
        return (int)(((n % mod) * (n % mod)) % mod);
    }
    private static final Scanner scanner = new Scanner(System.in);
    public static void main(String[] args) throws IOException {
        BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
        int t = Integer.parseInt(scanner.nextLine().trim());
        for (int tItr = 0; tItr < t; tItr++) {
            long n = Long.parseLong(scanner.nextLine().trim());
            int result = summingSeries(n);
            bufferedWriter.write(String.valueOf(result));
            bufferedWriter.newLine();
        }
        bufferedWriter.close();
    }
} 
solved Java : Summing the N series fails due to timeout