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Formula use:
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
Here, given expression is :
\left(x-1\right)\left(x^2+x+1\right)+\left(y-1\right)\left(y^2+y+1\right)+\left(z-1\right)\left(z^2+z+1\right)
\rightarrow\{\left(x\right)^3-\left(1\right)^3\}+\{\left(y\right)^3-\left(1\right)^3\}+\{\left(z\right)^3-\left(1\right)^3\}
\rightarrow\left(x^3-1^3+y^3-1^3+z^3-1^3\right)
\therefore x^3+y^3+z^3-3
Ans: x^3+y^3+z^3-3.
