<s>[INST] Visualizing $3^3+4^3+5^3=6^3$ I was wondering how would the visualization of $3^3+4^3+5^3=6^3$ look? I tried some 3D sketches but when calculating none work. Any ideas would be highly appreciated.
 [/INST] $$ 5^3 + 3^3 + 4^3  = 5^3 + 3 \cdot (3^2 + 4^2) + 4^2 = 5^3 + 3 \cdot 5^2 + 3 \cdot 5 + 1 = (5 + 1)^3 $$ 
So a cube of side $6$ units can be made by taking a $\color{green}{\text{cube of side 5  units} }$, adding $ \color{blue}{\text{3 5-by-5 squares}}$   at the top, right and left, then adding $\color{red}{\text{3 lines of length 5}}$ along $3$ edges and finally adding $\color{black}{ \text{1 cube} }$ at the corner.

Source of picture of cube 
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