601 Cubed

601 cubed, (601)³, is the number you get when multiplying 601 times 601 times 601.

It can also be looked at as exponentiation involving the base 601 and the exponent 3.

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

The cube of 601 is a perfect cube because the number is the product of the three equal integers 601.

It can be written as 601 × 601 × 601 or in exponential form.

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

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(601)³ = 217,081,801
601 × 601 × 601 = 217,081,801
The inverse operation of cubing 601 is extracting the cube root of 601, explained here.

In the next section we elaborate on the cube 601.

What is 601 Cubed?

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

Hence, a cube with side length 601 has an area of 217,081,801.

The sum and the differences of two cubes, for example with side length 601 and 600, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 601, b = 600 and the equivalence we get:
   (601)³ = 1201 x (601² – 601 × 600 + 600²) – 600³ = 1201 x (361201 – 360600 + 360000) – 216000000 = 1201 x 360601 – 216000000 = 217,081,801
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 601, b = 600 and the equivalence we get:
   (601)³ = (601² + 601 × 600 + 600²) + 600³ = 361201 + 360600 + 360000 + 216000000 = 217,081,801

As follows from (1), 601 cubed can be calculated from 600 cubed and 601 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(601)³ = (2 × 601 – 1) × (601² – 601 + 1) – (600)³ = 1201 × (361201 – 600) – 216000000 = 1201 × 360601 – 216000000 = 217,081,801

Using the second formula 601 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(601)³ = 600³ + 3 × 601² – 3 × 601 + 1 = 216000000 + 3 × 361201 – 3 × 601 + 1 = 216000000 + 1083603 – 1803 + 1 = 217,081,801

If you want to calculate the cube of any number, not only integers like 601, you can use our calculator above.

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A cube similar to 601 is, for example: cube of 603.


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The following table contains the cubes of numbers close to 601.

Table

Six Hundred One Cubed

You now know everything about the cube 601 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

601 cubed is equivalent to 217,081,801.

If you were searching for what is 601 cubed in math or if you typed whats 601 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube601, and 601 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 601 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

601 cubed = 601 x 601 x 601 = (601)³ = 601 to the 3rd power = 217,081,801.

The exponentiation form is mostly used to denote 601 cube.

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