Sum of Cubes and Cube of Sum Calculator

Enter a set of data to calculate the sum of cubes and the cube of the sum.

Calculate the Sum of Cubes and Cube of Sum

Sum of Cubes

Cube of Sum

How to Calculate the Sum of Cubes and the Cube of the Sum?

1. Sum of Cubes

The sum of cubes refers to cubing each number in a data set and then adding up all the cube values. For a set of numbers \( X, Y, Z \), the formula for the sum of cubes is: \( \text{Sum of Cubes} = X^3 + Y^3 + Z^3 \) This formula can be applied to any number of values, and the result will be the total sum of each number cubed.

2. Cube of the Sum

The cube of the sum refers to first calculating the sum of all the numbers in the data set, and then cubing the result. For a set of numbers \( X, Y, Z \), the formula for the cube of the sum is: \( \text{Cube of the Sum} = (X + Y + Z)^3 \) The cube of the sum is used to amplify the result of adding all the numbers, especially when you need to perform cubic analysis on the total sum of the data.

Custom Delimiters Explanation

This calculator can automatically handle common numeric delimiters such as commas, spaces, semicolons, line breaks, etc. If the data uses a special delimiter, such as "|" or any other symbol, you can manually enter the custom delimiter. Additionally, note that the thousand separator and number separator should not be the same to ensure accurate calculations.

Examples

Example 1: For the data set \( [2, 3, 4] \), calculate the sum of cubes and the cube of the sum.

Solution:

1. Sum of Cubes:

\( 2^3 + 3^3 + 4^3 = 8 + 27 + 64 = 99 \)

Result: Sum of Cubes = 99

2. Cube of the Sum:

\( (2 + 3 + 4)^3 = (9)^3 = 729 \)

Result: Cube of the Sum = 729

Example 2: For the data set \( [5, 7, 9] \), calculate the sum of cubes and the cube of the sum.

Solution:

1. Sum of Cubes:

\( 5^3 + 7^3 + 9^3 = 125 + 343 + 729 = 1197 \)

Result: Sum of Cubes = 1197

2. Cube of the Sum:

\( (5 + 7 + 9)^3 = (21)^3 = 9261 \)

Result: Cube of the Sum = 9261

Example 3: For the data set \( [10, 20, 30, 40, 50] \), calculate the sum of cubes and the cube of the sum.

Solution:

1. Sum of Cubes:

\( 10^3 + 20^3 + 30^3 + 40^3 + 50^3 = 1000 + 8000 + 27000 + 64000 + 125000 = 225000 \)

Result: Sum of Cubes = 225000

2. Cube of the Sum:

\( (10 + 20 + 30 + 40 + 50)^3 = (150)^3 = 3375000 \)

Result: Cube of the Sum = 3375000