64 Cubed

64 cubed, (64)³, is the number you get when multiplying 64 times 64 times 64.

It can also be looked at as exponentiation involving the base 64 and the exponent 3.

The term is usually pronounced 3rd power of sixty-four or sixty-four cubed.

The cube of 64 is a perfect cube because the number is the product of the three equal integers 64.

It can be written as 64 × 64 × 64 or in exponential form.

Read on to learn everything about the number sixty-four cubed, including useful identities.

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(64)³ = 262,144
64 × 64 × 64 = 262,144
The inverse operation of cubing 64 is extracting the cube root of 64, explained here.

In the next section we elaborate on the cube 64.

What is 64 Cubed?

A cube is a three-dimensional shape with 6 equal square faces.

Hence, a cube with side length 64 has an area of 262,144.

The sum and the differences of two cubes, for example with side length 64 and 63, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 64, b = 63 and the equivalence we get:
   (64)³ = 127 x (64² – 64 × 63 + 63²) – 63³ = 127 x (4096 – 4032 + 3969) – 250047 = 127 x 4033 – 250047 = 262,144
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 64, b = 63 and the equivalence we get:
   (64)³ = (64² + 64 × 63 + 63²) + 63³ = 4096 + 4032 + 3969 + 250047 = 262,144

As follows from (1), 64 cubed can be calculated from 63 cubed and 64 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(64)³ = (2 × 64 – 1) × (64² – 64 + 1) – (63)³ = 127 × (4096 – 63) – 250047 = 127 × 4033 – 250047 = 262,144

Using the second formula 64 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(64)³ = 63³ + 3 × 64² – 3 × 64 + 1 = 250047 + 3 × 4096 – 3 × 64 + 1 = 250047 + 12288 – 192 + 1 = 262,144

If you want to calculate the cube of any number, not only integers like 64, you can use our calculator above.

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A cube similar to 64 is, for example: cube of 66.


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The following table contains the cubes of numbers close to 64.

Table

Sixty-Four Cubed

You now know everything about the cube 64 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

64 cubed is equivalent to 262,144.

If you were searching for what is 64 cubed in math or if you typed whats 64 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube64, and 64 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 64 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

64 cubed = 64 x 64 x 64 = (64)³ = 64 to the 3rd power = 262,144.

The exponentiation form is mostly used to denote 64 cube.

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– Article written by Mark, last updated on November 26th, 2023