Given $a+b+c$, Can I calculate $a^2+b^2+c^2$? I want to calculate $a^2 + b^2 + c^2$  when I am given $a+b+c$.
It is known that a,b,c are positive integers.
Is there any way to find that.

No. Suppose that $a+b+c = 6$. 
If $a = b = c = 2$, then $a^2 + b^2 + c^2 = 12$.
If $a = 4$ and $b = c = 1$, then $a^2 + b^2 + c^2 = 18$
The sum of the squares varies for a given sum of $a$, $b$, and $c$.
