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16 cubed, (16)3, is the number you get when multiplying 16 times 16 times 16.
It can also be looked at as exponentiation involving the base 16 and the exponent 3.
The term is usually pronounced 3rd power of sixteen or sixteen cubed.
The cube of 16 is a perfect cube because the number is the product of the three equal integers 16.
It can be written as 16 × 16 × 16 or in exponential form.
Read on to learn everything about the number sixteen cubed, including useful identities.
Calculator
16 × 16 × 16 = 4,096
The inverse operation of cubing 16 is extracting the cube root of 16, explained here.
In the next section we elaborate on the cube 16.
What is 16 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 16 has an area of 4,096.
The sum and the differences of two cubes, for example with side length 16 and 15, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 16, b = 15 and the equivalence we get:
(16)3 = 31 x (162 – 16 × 15 + 152) – 153 = 31 x (256 – 240 + 225) – 3375 = 31 x 241 – 3375 = 4,096 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 16, b = 15 and the equivalence we get:
(16)3 = (162 + 16 × 15 + 152) + 153 = 256 + 240 + 225 + 3375 = 4,096
As follows from (1), 16 cubed can be calculated from 15 cubed and 16 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(16)3 = (2 × 16 – 1) × (162 – 16 + 1) – (15)3 = 31 × (256 – 15) – 3375 = 31 × 241 – 3375 = 4,096
Using the second formula 16 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(16)3 = 153 + 3 × 162 – 3 × 16 + 1 = 3375 + 3 × 256 – 3 × 16 + 1 = 3375 + 768 – 48 + 1 = 4,096
If you want to calculate the cube of any number, not only integers like 16, you can use our calculator above.
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A cube similar to 16 is, for example: cube of 18.
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The following table contains the cubes of numbers close to 16.
Table
| Number | Cube |
|---|---|
| 11 | 1,331 |
| 12 | 1,728 |
| 13 | 2,197 |
| 14 | 2,744 |
| 15 | 3,375 |
| 16 | 4,096 |
| 17 | 4,913 |
| 18 | 5,832 |
| 19 | 6,859 |
| 20 | 8,000 |
| 21 | 9,261 |
Sixteen Cubed
You now know everything about the cube 16 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
16 cubed is equivalent to 4,096.
If you were searching for what is 16 cubed in math or if you typed whats 16 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube16, and 16 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 16 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
16 cubed = 16 x 16 x 16 = (16)3 = 16 to the 3rd power = 4,096.
The exponentiation form is mostly used to denote 16 cube.
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– Article written by Mark, last updated on November 26th, 2023