101 LearnersLast updated on June 3rd, 2025
Cube of 63
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 63.
Cube of 63
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 by itself three times results in a negative number. The cube of 63 can be written as 63³, which is the exponential form. Or it can also be written in arithmetic form as, 63 × 63 × 63.
How to Calculate the Value of Cube of 63
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.
- 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 two 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.
63³ = 63 × 63 × 63
Step 2: You get 250,047 as the answer.
Hence, the cube of 63 is 250,047.
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 63 into two parts, as 60 and 3.
Let a = 60 and b = 3, so a + b = 63
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ , 3a²b = 3 × 60² × 3 , 3ab² = 3 × 60 × 3² , b³ = 3³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(60 + 3)³ = 60³ + 3 × 60² × 3 + 3 × 60 × 3² + 3³
63³ = 216,000 + 32,400 + 3,240 + 27 63³
= 250,047
Step 5: Hence, the cube of 63 is 250,047.
Using a Calculator
To find the cube of 63 using a calculator, input the number 63 and use the cube function (if available) or multiply 63 × 63 × 63. This operation calculates the value of 63³, resulting in 250,047. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 3
Step 3: If the calculator has a cube function, press it to calculate 63³.
Step 4: If there is no cube function on the calculator, simply multiply 63 three times manually.
Step 5: The calculator will display 250,047.
Tips and Tricks for the Cube of 63
- 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 63
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:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 63 × 63 and not 63 × 63 × 63. Always remember that 63³ = 63 × 63 × 63.
Solved Examples on Cube of 63
Problem 1
What is the cube and cube root of 63?
The cube of 63 is 250,047 and the cube root of 63 is approximately 3.979.
Explanation
First, let’s find the cube of 63.
We know that cube of a number, such that x³ = y
Where x is the given number, and y is the cubed value of that number So, we get 63³ = 250,047
Next, we must find the cube root of 63
We know that cube root of a number ‘x’, 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√63 ≈ 3.979
Hence the cube of 63 is 250,047 and the cube root of 63 is approximately 3.979.
Problem 2
If the side length of the cube is 63 cm, what is the volume?
The volume is 250,047 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 63 for the side length: V = 63³ = 250,047 cm³.
Problem 3
How much larger is 63³ than 53³?
63³ – 53³ = 125,047.
Explanation
First, find the cube of 63³, that is 250,047
Next, find the cube of 53³, which is 125,000
Now, find the difference between them using the subtraction method.
250,047 – 125,000 = 125,047
Therefore, the 63³ is 125,047 larger than 53³.
Problem 4
If a cube with a side length of 63 cm is compared to a cube with a side length of 13 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 63 cm is 250,047 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 63 means multiplying 63 by itself three times: 63 × 63 = 3,969, and then 3,969 × 63 = 250,047.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 250,047 cm³.
Problem 5
Estimate the cube 62.9 using the cube 63.
The cube of 62.9 is approximately 250,047.
Explanation
First, identify the cube of 63.
The cube of 63 is 63³ = 250,047.
Since 62.9 is only a tiny bit less than 63, the cube of 62.9 will be almost the same as the cube of 63.
The cube of 62.9 is approximately 250,047 because the difference between 62.9 and 63 is very small.
So, we can approximate the value as 250,047.
FAQs on Cube of 63
1.What are the perfect cubes up to 63?
2.How do you calculate 63³?
3.What is the meaning of 63³?
4.What is the cube root of 63?
5.Is 63 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 63?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 63?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 63
- 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 to 8.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- Perfect Cube: A perfect cube is an integer that can be expressed as the cube of another integer.
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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.
