Every square number is the sum of 2 triangular numbers, so (3) is the same as (1) (and so the last time this happened was 1936 (946 + 990)). Also, I think you're off by one in your rows.
Good point, will edit. There are a few nice properties around squared triangular numbers, so thought worth highlighting even if one follows from another.
I also liked this, via https://bsky.app/profile/peterwmurphy1.bsky.social/post/3leoppncids2u
1³+2³+3³+4³+5³+6³+7³+8³+9³=2025
Adam, Happy New Year! I am looking forward to the answer of your question and will work it backward.
Every square number is the sum of 2 triangular numbers, so (3) is the same as (1) (and so the last time this happened was 1936 (946 + 990)). Also, I think you're off by one in your rows.
Good point, will edit. There are a few nice properties around squared triangular numbers, so thought worth highlighting even if one follows from another.