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squares The picture illustrates the formula for the sum of the first six cube numbers:

$1^3 + 2^3 + 3^3 + ... + 6^3 = ( 1+ 2 + 3 + ... + 6)^2 $


Can you see which parts of the picture represent each part of the formula?

Could you draw a similar picture to represent the sum of the first seven cube numbers?

What about other sums of cubes?

Suggest a formula for the sum of the first $n$ cube numbers. Can you prove that your formula works, using diagrams and explanations? Send us your thoughts!