If (a-b)² + (b-c)² + (c-a)² = 0, then find the value of (a³+b³+c³-3abc) ?

If a =500, b=502 and c=504, then the value of a³ +b³ +c³-3abc

If average of two x and $$1\over x$$ (where x ≠ 0) is A, what will be the average of x³ and $$1\over {x^3}$$?

If $$ {4p\over{{p^2}}-4p+4}={1\over8}$$, p≠0 then the value of $$ {p+{4\over p}}$$

If  $$\sqrt{a}+\sqrt{b}=15 \ and \ (\sqrt{a}-\sqrt{b} )=3$$ then the value of $$\sqrt{ab/4} $$ is 

Value of $$ \sqrt{6+\sqrt {6+\sqrt {6+....}}}$$

If (a-b)=-3 , (b-c)=5 and (c-a)=-2, then the value of $$ {a^{3}+b^{3}+c^{3}-3abc\over a+b+c}$$.

If a + a²+a³-1=0, then what is the value of a³ +(1/a)?