504 Cubed

504 cubed, (504)³, is the number you get when multiplying 504 times 504 times 504.

It can also be looked at as exponentiation involving the base 504 and the exponent 3.

The term is usually pronounced 3rd power of five hundred four or five hundred four cubed.

The cube of 504 is a perfect cube because the number is the product of the three equal integers 504.

It can be written as 504 × 504 × 504 or in exponential form.

Read on to learn everything about the number five hundred four cubed, including useful identities.

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(504)³ = 128,024,064
504 × 504 × 504 = 128,024,064
The inverse operation of cubing 504 is extracting the cube root of 504, explained here.

In the next section we elaborate on the cube 504.

What is 504 Cubed?

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

Hence, a cube with side length 504 has an area of 128,024,064.

The sum and the differences of two cubes, for example with side length 504 and 503, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 504, b = 503 and the equivalence we get:
   (504)³ = 1007 x (504² – 504 × 503 + 503²) – 503³ = 1007 x (254016 – 253512 + 253009) – 127263527 = 1007 x 253513 – 127263527 = 128,024,064
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 504, b = 503 and the equivalence we get:
   (504)³ = (504² + 504 × 503 + 503²) + 503³ = 254016 + 253512 + 253009 + 127263527 = 128,024,064

As follows from (1), 504 cubed can be calculated from 503 cubed and 504 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(504)³ = (2 × 504 – 1) × (504² – 504 + 1) – (503)³ = 1007 × (254016 – 503) – 127263527 = 1007 × 253513 – 127263527 = 128,024,064

Using the second formula 504 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(504)³ = 503³ + 3 × 504² – 3 × 504 + 1 = 127263527 + 3 × 254016 – 3 × 504 + 1 = 127263527 + 762048 – 1512 + 1 = 128,024,064

If you want to calculate the cube of any number, not only integers like 504, you can use our calculator above.

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A cube similar to 504 is, for example: cube of 506.


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The following table contains the cubes of numbers close to 504.

Table

Five Hundred Four Cubed

You now know everything about the cube 504 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

504 cubed is equivalent to 128,024,064.

If you were searching for what is 504 cubed in math or if you typed whats 504 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube504, and 504 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 504 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

504 cubed = 504 x 504 x 504 = (504)³ = 504 to the 3rd power = 128,024,064.

The exponentiation form is mostly used to denote 504 cube.

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