An Observation

An observation: If you add 3 numbers, make it's cube. Subtract from it individual cubes of these 3 numbers the answer of subtraction will always be divisible by 3.

Cuberoots of cubes of 10 to 99 in 15 seconds!

How to quickly find cube root?
Tell your friend to take any 2 digit number and calculate its cube. Tell him to tell you the answer I.e. give you the perfect cube number.
Step 1:Note the last (unit place) digit. If it is 0,1,4,5,6 or 9 the unit place digit of cube root is the last digit itself. If it is 2,3,7 or 8 the last digit of the cube root is 8,7,3 or 2 respectively.
Step 2:Leave aside the last 3 digits of the perfect cube from right.
Step 3: Consider the remaining number. This number will be maximum a 3 digit number. (Learn by heart cubes of 0 to 9). Find the largest perfect cube smaller than this considered number.
Step 4: The cube root of this largest perfect cube is the tens place digit of the cube root of the number given by your friend.
Step 5: write step 4's answer. To its right write answer of steps 1.
Step 6: This is the answer. I.e. the 2 digit number originally taken by your friend. I mean the cube root of the number told (given) by your friend.