Last updated on June 2nd, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 507.
A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number multiplied by itself three times results in a negative number. The cube of 507 can be written as 507³, which is the exponential form. Or it can also be written in arithmetic form as, 507 × 507 × 507.
In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.
The multiplication method is a process in mathematics used to find the product of numbers by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number.
507³ = 507 × 507 × 507
Step 2: You get 130,515,843 as the answer.
Hence, the cube of 507 is 130,515,843.
The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 507 into two parts.
Let a = 500 and b = 7, so a + b = 507
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³= 500³ , 3a²b = 3 × 500² × 7 , 3ab² = 3 × 500 × 7² , b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 7)³ = 500³ + 3 × 500² × 7 + 3 × 500 × 7² + 7³ 507³
= 125,000,000 + 5,250,000 + 73,500 + 343 507³
= 130,515,843
Step 5: Hence, the cube of 507 is 130,515,843.
To find the cube of 507 using a calculator, input the number 507 and use the cube function (if available) or multiply 507 × 507 × 507. This operation calculates the value of 507³, resulting in 130,515,843. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5 followed by 0 then 7
Step 3: If the calculator has a cube function, press it to calculate 507³.
Step 4: If there is no cube function on the calculator, simply multiply 507 three times manually.
Step 5: The calculator will display 130,515,843.
The cube of any even number is always even, while the cube of any odd number is always odd. The product of two or more perfect cube numbers is always a perfect cube. A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:
What is the cube and cube root of 507?
The cube of 507 is 130,515,843 and the cube root of 507 is approximately 7.986.
First, let’s find the cube of 507.
We know that the cube of a number is x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 507³ = 130,515,843
Next, we must find the cube root of 507.
We know that the cube root of a number ‘x’ is such that ³√x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ³√507 ≈ 7.986
Hence, the cube of 507 is 130,515,843 and the cube root of 507 is approximately 7.986.
If the side length of a cube is 507 cm, what is the volume?
The volume is 130,515,843 cm³.
Use the volume formula for a cube V = Side³.
Substitute 507 for the side length: V = 507³ = 130,515,843 cm³.
How much larger is 507³ than 407³?
507³ – 407³ = 88,514,843.
First find the cube of 507, which is 130,515,843.
Next, find the cube of 407, which is 42,001,000.
Now, find the difference between them using the subtraction method: 130,515,843 – 42,001,000 = 88,514,843.
Therefore, 507³ is 88,514,843 larger than 407³.
If a cube with a side length of 507 cm is compared to a cube with a side length of 107 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 507 cm is 130,515,843 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 507 means multiplying 507 by itself three times:
507 × 507 = 257,049, and then 257,049 × 507 = 130,515,843.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 130,515,843 cm³.
Estimate the cube of 506.9 using the cube of 507.
The cube of 506.9 is approximately 130,515,843.
First, identify the cube of 507, which is 507³ = 130,515,843.
Since 506.9 is only a tiny bit less than 507, the cube of 506.9 will be almost the same as the cube of 507.
The cube of 506.9 is approximately 130,515,843 because the difference between 506.9 and 507 is very small.
So, we can approximate the value as 130,515,843.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.