Every Cube is an Arithmetic Sum (visual proof without words)

This is a short, animated (wordless) visual proof demonstrating that every cube can be written as the sum of an arithmetic progression involving the triangular numbers T_n, which are the sum of the first n positive integers. #manim #proofwithoutwords #math #mathshorts​ #mathvideo​​ #mtbos​ ​ #animation​ #theorem​ #pww​​ #visualproof​ #proof​ #iteachmath #cubes #discretemath

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[kdicus]

Can you show visual proof for Would love to see the way your brain sees it.

[jakobthomsen]

Nice but feels somewhat incomplete: isn't it possible to rearrange the sum into something like
n * T_n + (0*n+1*n+2*n+...+(n-1)*n) = n * T_n + n * T_(n-1) = n * (T_n + T_(n-1))?

[christopherellis]

Sum if (1+6#)?
What you've presented here result in n², not n³