To solve this expression, we follow the order of operations (PEMDAS/BODMAS):

3⁶ : 3² + 2³ . 2 - 3³ . 3

First, we simplify the exponents:

3⁶ = 3 * 3 * 3 * 3 * 3 * 3 = 729
3² = 3 * 3 = 9
2³ = 2 * 2 * 2 = 8
3³ = 3 * 3 * 3 = 27

Now, we substitute these values back into the expression:

729 : 9 + 8 . 2 - 27 . 3

Next, we perform the multiplication and division from left to right:

729 : 9 + 16 - 81

Now, we perform the addition and subtraction from left to right:

81 + 16 - 81

Finally, we perform the remaining addition and subtraction:

97 - 81 = 16

Therefore, the value of the expression is 16.