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A 'cube' is when a number is raced to the third power, so 5 'cubed' is . A binomial is a polynomial with two  terms, so 3xyz + 12xyz is a binomial.

A cube of a binomial could possibly refer to something like this: 
0 0 0
5 cubed is 5^3 and a cube of a binomial is something like [3xyz +12xyz]^3
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