robinhouston on Nostr: Because it's 2025, we're all thinking about the identity ...

Because it's 2025, we're all thinking about the identity \[\Bigl(\sum_{i=0}^ni\Bigr)^2
=
\sum_{i=0}^ni^3\]

I'm now wondering how closely this is related to the similar (but in a way simpler) identity
\[
\Bigl(\int_{0}^nx\,dx\Bigr)^2
=
\int_{0}^nx^3\,dx
\]

Is the former a direct consequence of the latter?