static void printMaxHourglassSum(List> arr){ //System.out.println("arr " + (arr.get(0)).get(0));

    ArrayList<Integer> arrSum = new ArrayList<>();
    for(int row=0; row<6; row++){
        for(int col=0; col<6; col++){
            //System.out.println("row: " + row + ", col: " + col);
            int skipIdx = 0;
            int temp = 0;
            if(row<=3 && col<=3)
            {
                for(int i=row; i<row+3; i++){
                    for(int j=col; j<col+3; j++){
                        skipIdx++;
                        //System.out.println("idx: " + idx);
                        // System.out.println("i: " + i 
                        //     + ", j: " + j 
                        //     + "= " + (arr.get(i)).get(j));

                        if(skipIdx==4 ||skipIdx==6){
                            continue;
                        }

                        temp += (arr.get(i)).get(j);
                    }
                }
                //System.out.println("temp: " + temp);
                arrSum.add(temp);
            }
        }
    }

    for(int i=0; i<arrSum.size(); i++){
        //System.out.println("arrSum: " + arrSum.get(i));
    }

    Collections.sort(arrSum);

    System.out.println(arrSum.get(arrSum.size()-1));
}

All cases are OK, but the "congrulations" message does not appear.

public class Solution { public static void main(String[] args) throws IOException { BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    List<List<Integer>> arr = new ArrayList<>();

    for (int i = 0; i < 6; i++) {
        String[] arrRowTempItems = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");

        List<Integer> arrRowItems = new ArrayList<>();

        for (int j = 0; j < 6; j++) {
            int arrItem = Integer.parseInt(arrRowTempItems[j]);
            arrRowItems.add(arrItem);
        }

        arr.add(arrRowItems);
    }
    int maxSum = Integer.MIN_VALUE;
    for (int i = 0; i < 5; i++) {    

        for (int j = 0; j < 5; j++){ 

            if(i+2 < arr.size() && j+2 < arr.get(i).size()){

                int sum = arr.get(i).get(j) + arr.get(i).get(j+1) 
                        + arr.get(i).get(j+2) + arr.get(i+1).get(j+1)
                        + arr.get(i+2).get(j) + arr.get(i+2).get(j+1) 
                        + arr.get(i+2).get(j+2);

                            maxSum = Math.max(maxSum, sum);
            }
        }
    }
    System.out.print(maxSum);

    bufferedReader.close();
}

}

import java.util.*;

public class Solution { public static void main(String[] args) { Scanner sc = new Scanner(System.in); int[][] arr = new int[6][6];

    // Reading 6x6 array
    for (int i = 0; i < 6; i++) {
        for (int j = 0; j < 6; j++) {
            arr[i][j] = sc.nextInt();
        }
    }

    int maxSum = Integer.MIN_VALUE; // To handle negative numbers too

    // Loop through possible hourglass centers
    for (int i = 1; i < 5; i++) {
        for (int j = 1; j < 5; j++) {
            int sum = arr[i][j]                // middle
                    + arr[i-1][j-1] + arr[i-1][j] + arr[i-1][j+1] // top
                    + arr[i+1][j-1] + arr[i+1][j] + arr[i+1][j+1]; // bottom

            maxSum = Math.max(maxSum, sum);
        }
    }

    System.out.println(maxSum);
}

}

Using a matrix template to make this far more readable (and reusable):

public class Solution {
    private static void prettyPrint(List<List<Integer>> arr, int xOffset, int yOffset, int size) {
        for (int x=0; x<size; x++) {
            for (int y=0; y<size; y++) {
                System.out.print(arr.get(x + xOffset).get(y + yOffset) + " ");
            }
            System.out.println();
        }
    }
    
    private static int[][] hourglass = { {1, 1, 1},
                                         {0, 1, 0},
                                         {1, 1, 1} };
    
    private static int sumHourglass(List<List<Integer>> arr, int xOffset, int yOffset) {
        int sum = 0;
        for (int x=0; x<3; x++) {
            for (int y=0; y<3; y++) {
                if (hourglass[x][y]==1) {
                    sum += arr.get(x + xOffset).get(y + yOffset);
                }
            }
        }
        
        return sum;
    }
    
    public static void main(String[] args) throws IOException {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

        List<List<Integer>> arr = new ArrayList<>();

        final int n = 6;
        IntStream.range(0, n).forEach(i -> {
            try {
                arr.add(
                    Stream.of(bufferedReader.readLine().replaceAll("\\s+$", "").split(" "))
                        .map(Integer::parseInt)
                        .collect(toList())
                );
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        });

        bufferedReader.close();
        
        int max = Integer.MIN_VALUE;
        for (int x=0; x<=n-3; x++) {
            for (int y=0; y<=n-3; y++) {
//                prettyPrint(arr, x, y, 3);
                final int sum = sumHourglass(arr, x, y);
//                System.out.println(sum);
                if (sum>max) max = sum;
            }
        }
        
        System.out.println(max);

    }
}

import java.io.; import java.math.; import java.security.; import java.text.; import java.util.; import java.util.concurrent.; import java.util.function.; import java.util.regex.; import java.util.stream.*; import static java.util.stream.Collectors.joining; import static java.util.stream.Collectors.toList;

public class Solution { public static void main(String[] args) throws IOException { BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    List<List<Integer>> arr = new ArrayList<>();

    IntStream.range(0, 6).forEach(i -> {
        try {
            arr.add(
                Stream.of(bufferedReader.readLine().replaceAll("\\s+$", "").split(" "))
                    .map(Integer::parseInt)
                    .collect(toList())
            );
        } catch (IOException ex) {
            throw new RuntimeException(ex);
        }
    });

    int max = Integer.MIN_VALUE;
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < 4; j++) {
            int sum = arr.get(i).get(j) + arr.get(i).get(j + 1) + arr.get(i).get(j + 2) + arr.get(i + 1).get(j + 1)
                    + arr.get(i + 2).get(j) + arr.get(i + 2).get(j + 1) + arr.get(i + 2).get(j + 2);
                  max=Math.max(max,sum);

        }
    }
    System.out.println(max);
    bufferedReader.close();
}

}