"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?