Algebra Level pending

Let $$a,b,c$$ be the length of a triangle, such that $$a>b>c>0$$, $$b$$ is an integer and satisfy these equations:

• $$a+c = 2b$$
• $$a^{2} + b^{2} + c^{2} = 84$$

If the value of $$a+b-c$$ can be written as $$x+y\sqrt{z}$$ for integers $$x,y,z$$ and $$z$$ is square-free, find the value of $$x^{3}+y^{3}+z^{3}$$

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