Cubing numbers that are near a power of ten Such as 13, 104, 1012, etc.
Example: 123
Step One: Subtract the nearest power of ten from the number: 12 - 10 = 2
Step Two: Double this number and add the number being cubed: (2 x 2) + 12 = 16
Step Three: Subtract from this number the power of ten from step one: 16 - 10 = 6
Step Four: Multiply this number by the answer in step one: 2 x 6 = 12
Step Five: Cube the answer in step one: 23 = 8
Step Six: Since we're cubing a 2 digit number, add two zeros to the answer in step two: 1600
Step Seven: Add 1 zero to the answer in step four: 120
Step Eight: Add the answers in steps seven and eight to the answer in step five: 1600 + 120 + 8 = 1728
Thus, 123 = 1728
Cubing numbers that are near a multiple of a power of ten Such as 42, 507, 2008, etc.
Example: 483
Step One: Keep in mind that the main base is 10 and our working base will be 50
Step Two: Divide the main base by the working base: 10 / 50 = 1/5
Step Three: Subtract the working base from the number being squared: 48 - 50 = -2
Step Four: Double this number and add the number being squared: (-2 x 2) + 48 = 44
Step Five: Divide this number by the square of the ratio found in step two: 44 / (1/5)2 = 44 / (1/25) = 44 x 25 = 1100
Step Six: Subtract the working base from the answer in step four: 44 - 50 = -6
Step Seven: Multiply the answer in step three by the answer in step six: -2 x -6 = 12
Step Eight: Divide this number by the ratio in step two: 12 / (1/5) = 12 x 5 = 60
Step Nine: Cube the answer found in step three: -23 = -8
Step Ten: Since we're cubing a 2 digit number, add two zeros to the answer in step five: 110000
Step Eleven: Add 1 zero to the answer in step eight: 600
Step Twelve: Add the answers in steps ten and eleven to the answer in step nine: 110000 + 600 + -8 = 110592
Thus, 483 = 110592
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