# Classical Inequalities addicts can do this. Part 3

Algebra Level 4

Let $$a,b,c,d$$ be all real numbers such that $$a^3 + b^3 + c^3 + d^3 = 41$$ and $$\phi = a+b+c+d \ge 0$$.

What is the minimum value of $$\displaystyle \sum_{ a, \ b, \ c, \ d} (\phi - a)^3$$?

For more problems like this, try answering this set.

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