This week we have been looking at the sums of squares; here is a problem regarding the sums of cubes.

You have a cube with sides of length 5 units. You need to dissect it into smaller cubes, all with integer sides, in such a way that you can reconstruct the original cube. What is the minimum possible number of smaller cubes? List how many cubes of each size there are.

Remember that it is not enough for the sums of cubes to be arithmetically correct, the cubes need to all fit together to make the original cube with sides of length 5 units.

**Feel free to comment, ask questions and even check your answer in the comments box below powered by Disqus.**

**If you enjoy using this website then please consider making a donation - every little helps :-)**

**You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.**

**Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..**

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.