Tell me... what's 6 x 6?
Now don't tell me you don't have that memorized and worked it out in your head.

Up until the equivalent of your fifth grade, I never bothered to memorize the multiplication table. Any time faced with a multiplication problem, I worked it out using first principles. Sometimes I use analytical shortcuts to derive the answer, but never from rote memorization. For example in the case of 6 x 6, this was how I used to work it out:

1) First, realize that [a number] x 6 is [a number] x (5 + 1) = [a number] x 5 + [a number]

2) Also realize that [a number] x 5 is [a number] x (10/2) = [a number / 2] x 10

3) Now visualize 6 apples lined up in a row. Now visualize a line running through the middle of that row of apples. How many apples are on each side? 3, of course

4) Now take the number 3 and put 0 at the end of it. Now you have 30, which is 6 x 5.

5) Now take 30 + 6 and you have 36, which is the answer to 6 x 6.

Now isn't that more fun than memorizing the multiplication table?