my solution for C (Sorry if it's messy, I'm fairly new to this):

(for testcases 3 & 7, maxsum is negative, so make sure it is not initilized to zero. I initilized to the first hourglass sum)

int main() {
int a[6][6], i, j, k, m, sum, maxsum;  
for (i = 0; i < 6; i++){
    for (j = 0; j < 6 ; j++){
        scanf("%d", &a[i][j]);
    }
}

maxsum = a[0][0]+a[0][1]+a[0][2]+a[1][1]+a[2][0]+a[2][1]+a[2][2]; //sum of first hourglass

for (i = 0; i < 4; i++){ // i is the top row of hourglass

  for (j = 0; j < 4; j++){ //moves hourglass one to right

      sum = 0; //resets sum for new hourglass

      for (k = j; k < j+3; k++){ // value for column

          sum += a[i][k]; //sum of first row

          if (k == j+1){ // middle row of hourglass
              sum += a[i+1][k]; //sum of middle row
          }

          m = i+2; // third row of hourglass
          sum += a[m][k]; //sum of third row
      }

    if (sum > maxsum){ // if new sum is greater than maxsum

          maxsum = sum; // sum becomes the new maxsum
    }
  }
 }
  printf("%d", maxsum);
}

(indentention got messed up @ end when copypaste, sry)