"A Mathematician's Apology"

Algebra Level 3

Find the value of the sum of 100 first cubes:

13+23+33+43+53++1003 { 1 }^{ 3 }+{ 2 }^{ 3 }+{ 3 }^{ 3 }+{ 4 }^{ 3 }+{ 5 }^{ 3 }+\cdots+{ 100 }^{ 3 }

Bonus: Could you generalize this for the first nn cubes?

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