1000 Cubed


1000 cubed, 10003, is the number you get when multiplying 1000 times 1000 times 1000. It can also be looked at as exponentiation involving the base 1000 and the exponent 3. The term is usually pronounced 3rd power of thousand or thousand cubed. The cube of 1000 is a perfect cube because the number is the product of the three equal integers 1000. It can be written as 1000 x 1000 x 1000 or in exponential form. Read on to learn everything about the number thousand cubed, including useful identities.

10003 = 1000000000
1000 x 1000 x 1000 = 1000000000

The inverse operation of cubing 1000 is extracting the cube root of 1000, explained here. In the next section we elaborate on the cube 1000, and there you can also find our calculator.

What is 1000 Cubed

A cube is a three-dimensional shape with 6 equal square faces. Hence, a cube with side length 1000 has an area of 1000000000.

The sum and the differences of two cubes, for example with side length 1000 and 999, can be calculated with the following formulas:

  1. a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
    With a = 1000, b = 999 and the equivalence we get:
    10003 = 1999 x (10002 – 1000 × 999 + 9992) – 9993 = 1999 x (1000000 – 999000 + 998001) – 997002999 = 1999 x 999001 – 997002999 = 1000000000
  2. a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
    With a = 1000, b = 999 and the equivalence we get:
    10003 = (10002 + 1000 × 999 + 9992) + 9993 = 1000000 + 999000 + 998001 + 997002999 = 1000000000

As follows from (1), 1000 cubed can be calculated from 999 cubed and 1000 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
10003 = (2 × 1000 – 1) × (10002 – 1000 + 1) – (999)3 = 1999 × (1000000 – 999) – 997002999 = 1999 × 999001 – 997002999 = 1000000000

Using the second formula 1000 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1
10003 = 9993 + 3 × 10002 – 3 × 1000 + 1 = 997002999 + 3 × 1000000 – 3 × 1000 + 1 = 997002999 + 3000000 – 3000 + 1 = 1000000000

If you want to calculate the cube of any number, not only integers like 1000, you can use our calculator below. Just enter your number; the calculation is then done automatically.

Calculate Cubed Number

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If this tool has been beneficial to you, then bookmark it right now. Besides the cube of 1000, more searched cubes on our site include:

1000 Cubed

Thousand Cubed

You now know everything about the cube 1000 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities: 1000 cubed is equivalent to 1000000000.

If you were searching for what is 1000 cubed in math or if you typed whats 1000 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube1000, and 1000 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 1000 cubed using the search form in the sidebar of this page.

To sum up,

1000 cubed = 1000x1000x1000 = 10003 = 1000 to the 3rd power = 1000000000. The exponentiation form is mostly used to denote 1000 cube.

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