Cube of 513
2026-02-28 11:21 Diff
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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 513.

Cube of 513

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 513 can be written as 513³, which is the exponential form. Or it can also be written in arithmetic form as, 513 × 513 × 513.

How to Calculate the Value of Cube of 513

To check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help students cube numbers faster and more easily without feeling confused or stuck while evaluating the answers.

  • By Multiplication Method
     
  • Using a Formula
     
  • Using a Calculator

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number.

513³ = 513 × 513 × 513

Step 2: You get 135,796,257 as the answer.

Hence, the cube of 513 is 135,796,257.

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Using a Formula (a³)

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 513 into two parts.

Let a = 500 and b = 13, so a + b = 513

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 13 , 3ab² = 3 × 500 × 13² , b³ = 13³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(500 + 13)³ = 500³ + 3 × 500² × 13 + 3 × 500 × 13² + 13³

513³ = 125,000,000 + 97,500 + 101,400 + 2,197

513³ = 135,796,097

Step 5: Hence, the cube of 513 is 135,796,257.

Using a Calculator

To find the cube of 513 using a calculator, input the number 513 and use the cube function (if available) or multiply 513 × 513 × 513. This operation calculates the value of 513³, resulting in 135,796,257. 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 1 and 3.

Step 3: If the calculator has a cube function, press it to calculate 513³.

Step 4: If there is no cube function on the calculator, simply multiply 513 three times manually.

Step 5: The calculator will display 135,796,257.

Tips and Tricks for the Cube of 513

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.

Common Mistakes to Avoid When Calculating the Cube of 513

There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:

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Problem 1

What is the cube and cube root of 513?

Okay, lets begin

The cube of 513 is 135,796,257 and the cube root of 513 is approximately 8.051.

Explanation

First, let’s find the cube of 513.

We know that the cube of a number is such that x³ = y.

Where x is the given number, and y is the cubed value of that number.

So, we get 513³ = 135,796,257.

Next, we must find the cube root of 513.

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√513 ≈ 8.051.

Hence the cube of 513 is 135,796,257 and the cube root of 513 is approximately 8.051.

Well explained 👍

Problem 2

If the side length of a cube is 513 cm, what is the volume?

Okay, lets begin

The volume is 135,796,257 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 513 for the side length: V = 513³ = 135,796,257 cm³.

Well explained 👍

Problem 3

How much larger is 513³ than 413³?

Okay, lets begin

513³ – 413³ = 88,515,793.

Explanation

First find the cube of 513, that is 135,796,257.

Next, find the cube of 413, which is 47,280,464.

Now, find the difference between them using the subtraction method.

135,796,257 – 47,280,464 = 88,515,793.

Therefore, 513³ is 88,515,793 larger than 413³.

Well explained 👍

Problem 4

If a cube with a side length of 513 cm is compared to a cube with a side length of 113 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 513 cm is 135,796,257 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 513 means multiplying 513 by itself three times.

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

Therefore, the volume of the cube is 135,796,257 cm³.

Well explained 👍

Problem 5

Estimate the cube of 512.9 using the cube of 513.

Okay, lets begin

The cube of 512.9 is approximately 135,796,257.

Explanation

First, identify the cube of 513.

The cube of 513 is 513³ = 135,796,257.

Since 512.9 is only a tiny bit less than 513, the cube of 512.9 will be almost the same as the cube of 513.

The cube of 512.9 is approximately 135,796,257 because the difference between 512.9 and 513 is very small.

So, we can approximate the value as 135,796,257.

Well explained 👍

FAQs on Cube of 513

1.What are the perfect cubes up to 513?

The perfect cubes up to 513 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 513³?

To calculate 513³, use the multiplication method: 513 × 513 × 513, which equals 135,796,257.

3.What is the meaning of 513³?

513³ means 513 multiplied by itself three times, or 513 × 513 × 513.

4.What is the cube root of 513?

5.Is 513 a perfect cube?

No, 513 is not a perfect cube because no integer multiplied by itself three times equals 513.

Important Glossaries for Cube of 513

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
  • Cube Root: The cube root of a number is a special value that, when multiplied by itself twice, gives the original number.
  • Perfect Cube: A number that is the cube of an integer. For example, 27 is a perfect cube because it is 3³.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.