631 Cubed

631 cubed, (631)³, is the number you get when multiplying 631 times 631 times 631.

It can also be looked at as exponentiation involving the base 631 and the exponent 3.

The term is usually pronounced 3rd power of six hundred thirty-one or six hundred thirty-one cubed.

The cube of 631 is a perfect cube because the number is the product of the three equal integers 631.

It can be written as 631 × 631 × 631 or in exponential form.

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

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(631)³ = 251,239,591
631 × 631 × 631 = 251,239,591
The inverse operation of cubing 631 is extracting the cube root of 631, explained here.

In the next section we elaborate on the cube 631.

What is 631 Cubed?

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

Hence, a cube with side length 631 has an area of 251,239,591.

The sum and the differences of two cubes, for example with side length 631 and 630, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 631, b = 630 and the equivalence we get:
   (631)³ = 1261 x (631² – 631 × 630 + 630²) – 630³ = 1261 x (398161 – 397530 + 396900) – 250047000 = 1261 x 397531 – 250047000 = 251,239,591
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 631, b = 630 and the equivalence we get:
   (631)³ = (631² + 631 × 630 + 630²) + 630³ = 398161 + 397530 + 396900 + 250047000 = 251,239,591

As follows from (1), 631 cubed can be calculated from 630 cubed and 631 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(631)³ = (2 × 631 – 1) × (631² – 631 + 1) – (630)³ = 1261 × (398161 – 630) – 250047000 = 1261 × 397531 – 250047000 = 251,239,591

Using the second formula 631 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(631)³ = 630³ + 3 × 631² – 3 × 631 + 1 = 250047000 + 3 × 398161 – 3 × 631 + 1 = 250047000 + 1194483 – 1893 + 1 = 251,239,591

If you want to calculate the cube of any number, not only integers like 631, you can use our calculator above.

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A cube similar to 631 is, for example: cube of 633.


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The following table contains the cubes of numbers close to 631.

Table

Six Hundred Thirty-One Cubed

You now know everything about the cube 631 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

631 cubed is equivalent to 251,239,591.

If you were searching for what is 631 cubed in math or if you typed whats 631 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube631, and 631 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 631 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

631 cubed = 631 x 631 x 631 = (631)³ = 631 to the 3rd power = 251,239,591.

The exponentiation form is mostly used to denote 631 cube.

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