How can I code a program to display, for example, $(a+b) ^ 3$ or $(a + b + c) ^ 3$ or $(a+b)^2$ or other variations of along the same lines.
A picture is worth more than 1000 words.
Here is a picture of $(a+b)^2$.
And here is one of $(a+b)^3$.
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This is not the most elegant code I've written but it's a fair start I think.
draw[HoldPattern[(+a__)^2]] := Module[{f1, n = Length[{a}]}, f1[i_] := {i - 1, i + 1} i/2; f1[i_, j_] := (f1 /@ {i, j})\[Transpose]; Graphics[{ EdgeForm[{Thick, Black}], Array[{RandomColor[], Rectangle @@ f1[##]} &, {n, n}], Array[Text[(1 a)[[{##}]], Mean @ f1[##]] &, {n, n}], Array[Text[(1 a)[[#]], {-1/4, Mean @ f1[#]}] &, n], Array[Text[(1 a)[[#]], {Mean @ f1[#], -1/4}] &, n] } ] ] draw[(a + b)^2] draw[(a + b + c)^2] draw[(a + b + c + d)^2] 
I just used
RandomColorfor the colors as I was not sure the the actual colors you wanted; if you clarify that I'll try to implement it.This is only for the 2D case but similar methods could be applied to the cubic case as well.
There is redundancy in this code but I felt that this form may be more readable than e.g. attempting to compress four
Arraycalls into two.
