"A Mathematician's Apology"

Algebra Level 3

Find the value of the sum of 100 first cubes:

\[ { 1 }^{ 3 }+{ 2 }^{ 3 }+{ 3 }^{ 3 }+{ 4 }^{ 3 }+{ 5 }^{ 3 }+\cdots+{ 100 }^{ 3 } \]

\[\] Bonus: Could you generalize this for the first \(n\) cubes?

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