Past, present, and future again

Algebra Level 3

Given

\[ \mathscr{E}(a, b, c) = a\big(b^3 - c^3 \big) + b\big(c^3 - a^3\big) + c\big(a^3 - b^3 \big), \]

find the value of \[ \dfrac{\mathscr{E} (2014, 2016, 2018)}{(2014 - 2016) (2014+2016+2018)}. \]

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