Sum of Cubes Calculator

What is Sum of Cubes?

The Sum of Cubes is like adding up the size of big blocks. Imagine you have different-sized toy blocks, and you want to know how much space they take up altogether. That's what the Sum of Cubes does!

How to Calculate Sum of Cubes

To find the Sum of Cubes, we take each number in our list and multiply it by itself three times. Then, we add up all these cubed numbers. It's like measuring each block and then adding up all their volumes.

Formula

We write the Sum of Cubes like this:

\[ \sum_{i=1}^{n} x_i^3 \]

This means:

• \(\sum\) is the big S that means "add up"
• \(i=1\) means we start with the first number
• \(n\) is how many numbers we have
• \(x_i\) is each number in our list
• \(x_i^3\) means we're cubing each number (multiplying it by itself three times)

Calculation Steps

1. Write down all your numbers
2. Cube each number (multiply it by itself three times)
3. Add up all these cubed numbers
4. The total is your Sum of Cubes!

Example and Visual Representation

Let's use an example with the numbers 2, 3, and 4:

2³ + 3³ + 4³ = 8 + 27 + 64 = 99

So, the Sum of Cubes is 99.

Let's show this with a picture:

In this picture, each colored cube represents the cube of a number. The red cube is 2³, the green cube is 3³, and the blue cube is 4³. When we add up the volumes of all these cubes, we get our Sum of Cubes, which is 99!