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6 cubed, (6)3, is the number you get when multiplying 6 times 6 times 6.
It can also be looked at as exponentiation involving the base 6 and the exponent 3.
The term is usually pronounced 3rd power of six or six cubed.
The cube of 6 is a perfect cube because the number is the product of the three equal integers 6.
It can be written as 6 × 6 × 6 or in exponential form.
Read on to learn everything about the number six cubed, including useful identities.
Calculator
6 × 6 × 6 = 216
The inverse operation of cubing 6 is extracting the cube root of 6, explained here.
In the next section we elaborate on the cube 6.
What is 6 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 6 has an area of 216.
The sum and the differences of two cubes, for example with side length 6 and 5, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 6, b = 5 and the equivalence we get:
(6)3 = 11 x (62 – 6 × 5 + 52) – 53 = 11 x (36 – 30 + 25) – 125 = 11 x 31 – 125 = 216 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 6, b = 5 and the equivalence we get:
(6)3 = (62 + 6 × 5 + 52) + 53 = 36 + 30 + 25 + 125 = 216
As follows from (1), 6 cubed can be calculated from 5 cubed and 6 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(6)3 = (2 × 6 – 1) × (62 – 6 + 1) – (5)3 = 11 × (36 – 5) – 125 = 11 × 31 – 125 = 216
Using the second formula 6 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(6)3 = 53 + 3 × 62 – 3 × 6 + 1 = 125 + 3 × 36 – 3 × 6 + 1 = 125 + 108 – 18 + 1 = 216
If you want to calculate the cube of any number, not only integers like 6, you can use our calculator above.
Just enter your number; nothing else to be done.
A cube similar to 6 is, for example: cube of 8.
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The following table contains the cubes of numbers close to 6.
Table
Number | Cube |
---|---|
1 | 1 |
2 | 8 |
3 | 27 |
4 | 64 |
5 | 125 |
6 | 216 |
7 | 343 |
8 | 512 |
9 | 729 |
10 | 1,000 |
11 | 1,331 |
Six Cubed
You now know everything about the cube 6 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
6 cubed is equivalent to 216.
If you were searching for what is 6 cubed in math or if you typed whats 6 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube6, and 6 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 6 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
6 cubed = 6 x 6 x 6 = (6)3 = 6 to the 3rd power = 216.
The exponentiation form is mostly used to denote 6 cube.
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– Article written by Mark, last updated on November 26th, 2023