Why do this
problem?
This is a tough
problem for learners who relish the challenge of working with
large and difficult numbers. It would become more accessible if
calculators were used.
Key questions
Have you found out how cubes are needed to cover the single
cube?
Have you remembered that there is only "up to $1000$ of each
colour"?
What is the cube root of $1000$?
Have you made list of the cubes up to $1000$?
Possible support
Suggest making starting by finding how many cubes are needed to
cover one (yellow) cube. This can be done practically with
interlocking cubes.