Happy New Year 2025 — the first year to be a square (whose digits sum to a square) that is equal to the sum of the first [sum of its digits] consecutive cubes and to the square of (and the product of the proper divisors of) the sum of a split of its digits.
If you add up the cube of every single-digit positive integer, the sum is 2025. Happy New Year!
1³+2³+3³+…..+9³ = Happy New Year
1) 2025, itself is a square
45²=2025
2) It’s a product of two squares,
Viz. 9² x 5² = 2025
3) It is the sum of 3-squares,
viz. 40²+ 20²+5²= 2025
4) It’s the first square after 1936
5) It’s the sum of cubes, of all the single digits, from 1 to 9,
viz. 1³+2³+3³+4³+5³+6³+7³+8³+9³= 2025.




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