# Sum of Distinct Cubes

Positive integers can be broken down into sums of distinct cubes of positive integers, sometimes in multiple different ways. Your function should find and return the descending list of distinct cubes whose sum equals the given positive integer **n**. If it is impossible to express **n** as a sum of distinct cubes, return **None**.

If **n** allows several breakdowns into sums of distinct cubes, the function must return the lexicographically highest solution that starts with the largest possible first number, followed by the lexicographically highest representation of the rest of the number **n-a*a*a**. For example, called with **n = 1729**, this function should return **[12, 1]** instead of **[10, 9]**.

**Input:** Positive integer (int).

**Output:** List of integers (int) or None.

**Examples:**

assert sum_of_cubes(1729) == [12, 1] assert sum_of_cubes(8) == [2] assert sum_of_cubes(11) == None

**Precondition:**

*n > 0*.

*The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen*

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin

checkio install-plugin --ff

checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.