Best Solution with Time Complexity O(n)

int sum;
int maxi = -100000;
int x = 0;
int y = 0;
for (int k = 1; k <= 16; k++) {

    sum = arr[y][x] + arr[y][x + 1] + arr[y][x + 2]
            + arr[y + 1][x + 1]
            + arr[y + 2][x] + arr[y + 2][x + 1] + arr[y + 2][x + 2];
    x++;

    if ((k % 4 == 0)) {
            x = 0;
            y++;
    }

    if(sum > maxi)
            maxi  = sum; 
}
System.out.println(maxi);