The picture illustrates the formula for the sum of the first six cube numbers: $1^3 + 2^3 + 3^3 + ... + 6^3 = ( 1+ 2 + 3 + ... + 6)^2$
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!