thanks to David Wells for the numerical approach
a ppt is here
this task can begin with an exploration of numbers
with a result being easy to find
it can be justifed using numbers
there is a novel diagrammatic representation
algebra can be tackled (if you can expand a cubic bracket) to justify the uniqueness of the first few results
or nrich 325
an interesting alternative diagram
possibly using Cuisenaire rods
algebra used to justify that you need to start at 1
(for the first two, three and four consecutive cube cases anyway)
the three consecutive cube case is easiest:
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