How to Cube a Number easily and quickly

The cube of a number is that number multiplied by itself twice. For example, 5 cubed - denoted as 5³; is equal to 5×5×5 = 125. The technique for cubing any 2-digit number discussed below is based on the algebraic observation.

Step-1:       Write numbers in a row of 4 terms in such a way that the first one is the cube of the 1^st digit, second one is the square of 1^st number multiplied by 2^nd digit, third one is the 1^st digit multiplied by square of 2^nd digit and the fourth one is the cube of the 2^nd digit.

Step-2:      Write twice the values of 2nd and 3rd terms under the terms respectively in second row.

Step-3:      Add all the values column-wise and follow the carry over process.

Example: Find Cube of 14.

Step-1                             :        1³       1²×4   1×4²   4³

Worked-out row               :        1        4        16      64

Step-2                             :                  8        32     

Step-3                             :        Add the values column wise.       

First Column from Right: Bring down 4 and carry over 6.

         

1	4 8	16 32	64
		6
			4

Second Column from Right: 16+32+6=54. Bring down 4 and carry over 5.               
                  

1	4 8	16 32	64
	5	6
		4	4

Third Column from Right: 4+8+5 = 17. Bring down 7 and carry over 1.            
                  

1	4 8	16 32	64
1	5	6
	7	4	4

Fourth Column from Right: 1 + 1 = 2. Write down 2.

1	4 8	16 32	64
1	5	6
2	7	4	4

This 2,744 is the cube of the number 14.

Another Example: Cube of 25 =?

         

Step-1		23	22×5	2×52	53
Worked-out		8	20	50	125
Step-2			40	100
Step-3	Carries
	Sum

First Column from Right: Bring down 5 and carry over 12.

         

8	20 40	50 100	125
		12
			5

Second Column from Right: 50 + 100 + 12 = 162. Bring down 2 and carry over 16.

8	20 40	50 100	125
	16	12
		2	5

Third Column from Right: 20 + 40+ 16 = 76. Bring down 6 and carry over 7.

8	20 40	50 100	125
7	16	12
	6	2	5

Fourth Column from Right: 8 + 7 = 15. Write down 15.

8	20 40	50 100	125
7	16	12
15	6	2	5

This 15,625 is the cube of the number 25.

Further example, 33³ =?

Step-1		33	32×3	3×32	33
Worked-out		27	27	27	27
Step-2			54	54
Step-3	Carries	8	8	2
	Sum	35	9	3	7

So, the cube of 33 is 35,937.

42³ =?                 

Step-1		64	32	16	8
Step-2			64	32
Step-3	Carries	10	4
	Sum	74	0	8	8

          So, the cube of 42 is 74,088.

89³ =?                 

83	82×9	8×92	93
512	576	648	729
	1152	1296
512	1728	1944	729

For convenient addition, you can write the values of each column total placing as many ‘zeros’ after the number as there are column(s) in the right and then add this way:

512000

172800

  19440

      729

704969

So, 89³ = 704,969

You can also cube a 3-digit number the same way, considering the first 2 digits as a single digit:

Say, 103³ =?

Step-1		103	102×3	10×32	33
Worked-out		1000	300	90	27
Step-2			600	180
Step-3	Carries	92	27	2
	Sum	1092	7	2	7

So, 103³ = 1,092,727