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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!