Subtract the following octal numbers: 737618 - 727778.

We have $1_8 - 7_8$. Since $1 < 7$, we borrow from the $6_8$ in the next column.
The $6_8$ becomes $5_8$. The $1_8$ becomes $1+8 = 9_{10}$.
Now, $9_{10} - 7_{10} = 2_{10}$. So the units digit is $2_8$.

We now have $5_8 - 7_8$. Since $5 < 7$, we borrow from the $7_8$ in the next column.
The $7_8$ becomes $6_8$. The $5_8$ becomes $5+8 = 13_{10}$.
Now, $13_{10} - 7_{10} = 6_{10}$. So the eights digit is $6_8$.

We now have $6_8 - 7_8$. Since $6 < 7$, we borrow from the $3_8$ in the next column.
The $3_8$ becomes $2_8$. The $6_8$ becomes $6+8 = 14_{10}$.
Now, $14_{10} - 7_{10} = 7_{10}$. So the $8^2$ digit is $7_8$.

We now have $2_8 - 2_8$.
$2_8 - 2_8 = 0_8$. So the $8^3$ digit is $0_8$.

We have $7_8 - 7_8$.
$7_8 - 7_8 = 0_8$. So the $8^4$ digit is $0_8$.

Combining the results from right to left:

The result is $00762_8$, which simplifies to $762_8$.