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643 Cubed

643 cubed, (643)3, is the number you get when multiplying 643 times 643 times 643.

It can also be looked at as exponentiation involving the base 643 and the exponent 3.

The term is usually pronounced 3rd power of six hundred forty-three or six hundred forty-three cubed.

The cube of 643 is a perfect cube because the number is the product of the three equal integers 643.

It can be written as 643 × 643 × 643 or in exponential form.

Read on to learn everything about the number six hundred forty-three cubed, including useful identities.

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(643)3 = 265,847,707
643 × 643 × 643 = 265,847,707

The inverse operation of cubing 643 is extracting the cube root of 643, explained here.

In the next section we elaborate on the cube 643.

What is 643 Cubed?

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

Hence, a cube with side length 643 has an area of 265,847,707.

The sum and the differences of two cubes, for example with side length 643 and 642, can be calculated with the following formulas:

  1. a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
    With a = 643, b = 642 and the equivalence we get:
    (643)3 = 1285 x (6432 – 643 × 642 + 6422) – 6423 = 1285 x (413449 – 412806 + 412164) – 264609288 = 1285 x 412807 – 264609288 = 265,847,707
  2. a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
    With a = 643, b = 642 and the equivalence we get:
    (643)3 = (6432 + 643 × 642 + 6422) + 6423 = 413449 + 412806 + 412164 + 264609288 = 265,847,707

As follows from (1), 643 cubed can be calculated from 642 cubed and 643 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(643)3 = (2 × 643 – 1) × (6432 – 643 + 1) – (642)3 = 1285 × (413449 – 642) – 264609288 = 1285 × 412807 – 264609288 = 265,847,707

Using the second formula 643 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1
(643)3 = 6423 + 3 × 6432 – 3 × 643 + 1 = 264609288 + 3 × 413449 – 3 × 643 + 1 = 264609288 + 1240347 – 1929 + 1 = 265,847,707

If you want to calculate the cube of any number, not only integers like 643, you can use our calculator above.

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A cube similar to 643 is, for example: cube of 645.


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The following table contains the cubes of numbers close to 643.

Table

NumberCube
638259,694,072
639260,917,119
640262,144,000
641263,374,721
642264,609,288
643265,847,707
644267,089,984
645268,336,125
646269,586,136
647270,840,023
648272,097,792

Six Hundred Forty-Three Cubed

You now know everything about the cube 643 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

643 cubed is equivalent to 265,847,707.

If you were searching for what is 643 cubed in math or if you typed whats 643 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube643, and 643 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 643 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

643 cubed = 643 x 643 x 643 = (643)3 = 643 to the 3rd power = 265,847,707.

The exponentiation form is mostly used to denote 643 cube.

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