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63 cubed, (63)3, is the number you get when multiplying 63 times 63 times 63.
It can also be looked at as exponentiation involving the base 63 and the exponent 3.
The term is usually pronounced 3rd power of sixty-three or sixty-three cubed.
The cube of 63 is a perfect cube because the number is the product of the three equal integers 63.
It can be written as 63 × 63 × 63 or in exponential form.
Read on to learn everything about the number sixty-three cubed, including useful identities.
Calculator
63 × 63 × 63 = 250,047
The inverse operation of cubing 63 is extracting the cube root of 63, explained here.
In the next section we elaborate on the cube 63.
What is 63 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 63 has an area of 250,047.
The sum and the differences of two cubes, for example with side length 63 and 62, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 63, b = 62 and the equivalence we get:
(63)3 = 125 x (632 – 63 × 62 + 622) – 623 = 125 x (3969 – 3906 + 3844) – 238328 = 125 x 3907 – 238328 = 250,047 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 63, b = 62 and the equivalence we get:
(63)3 = (632 + 63 × 62 + 622) + 623 = 3969 + 3906 + 3844 + 238328 = 250,047
As follows from (1), 63 cubed can be calculated from 62 cubed and 63 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(63)3 = (2 × 63 – 1) × (632 – 63 + 1) – (62)3 = 125 × (3969 – 62) – 238328 = 125 × 3907 – 238328 = 250,047
Using the second formula 63 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(63)3 = 623 + 3 × 632 – 3 × 63 + 1 = 238328 + 3 × 3969 – 3 × 63 + 1 = 238328 + 11907 – 189 + 1 = 250,047
If you want to calculate the cube of any number, not only integers like 63, you can use our calculator above.
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A cube similar to 63 is, for example: cube of 65.
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The following table contains the cubes of numbers close to 63.
Table
| Number | Cube |
|---|---|
| 58 | 195,112 |
| 59 | 205,379 |
| 60 | 216,000 |
| 61 | 226,981 |
| 62 | 238,328 |
| 63 | 250,047 |
| 64 | 262,144 |
| 65 | 274,625 |
| 66 | 287,496 |
| 67 | 300,763 |
| 68 | 314,432 |
Sixty-Three Cubed
You now know everything about the cube 63 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
63 cubed is equivalent to 250,047.
If you were searching for what is 63 cubed in math or if you typed whats 63 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube63, and 63 to the 3rd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect cubes including 63 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
63 cubed = 63 x 63 x 63 = (63)3 = 63 to the 3rd power = 250,047.
The exponentiation form is mostly used to denote 63 cube.
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– Article written by Mark, last updated on November 26th, 2023