With 2025 almost starting, I've seen a number of people talking about the fact that \(2025 = 45^2\), and since \(45\) is a triangular number, that gives rise to two fun formulas to compute \(2025\). First, since \(45\) is a triangular number, you get
\[ 2025 = 45^2 = (1 + 2 + 3 + \cdots + 8 + 9)^2 ~ .\]
The link to the Wikipedia page about squared triangular numbers also gives a beautiful geometrical demonstration that the formula above is equal to the sum of the cubes of the same integers:
\[ 2025 = 1^3 + 2^3 + 3^3 + \cdots + 8^3 + 9^3 ~ .\]