There are already answers, but I feel that something is missing...
When you make an assignment like
sum = a + b;
then the values of a and b are used to calculate the sum. This is the reason why a later change of one of the values does not change the sum. 
However, since C++11 there actually is a way to make your code behave the way you expect:
#include <iostream>     
int main() {
    int a = 5,b = 10;
    auto sum = [&](){return a + b;};
    b = 6;
    std::cout << sum(); 
    return 0;
}
This will print :
11
This line
auto sum = [&](){return a + b;};
declares a lambda. I cannot give a selfcontained explanation of lambdas here, but only some handwavy hints. After this line, when you write sum() then a and b are used to calculate the sum. Because a and b are captured by reference (thats the meaning of the &), sum() uses the current values of a and b and not the ones they had when you declared the lambda. So the code above is more or less equivalent to 
int sum(int a, int b){ return a+b;}
int main() {
    int a = 5,b = 10;
    b = 6;
    std::cout << sum(a,b);
    return 0;
}