GCC C++ pow accuracy

So i was in a computing contest and i noticed a weird bug. pow(26,2) would always return 675, and sometimes 674? even though correct answer is 676. These sort of errors also occur with pow(26,3), pow(26,4) etc After some debugging after the contest i believe the answer has to do with the fact int rounds down. Interestingly this kind of error has never occured to me before. The computer i had was running mingw on windows 8. GCC version was fairly new, like 2-3 months old i believe. But what i found was that if i turned the o1/o2/o3 optimization flag on these sort of error would miraculously disappear. pow(26,2) would always get 676 aka correct answer Can anyone explain why?

#include <cmath> 
#include <iostream> 

using namespace std; 
int main() { 
    cout<<pow(26,2)<<endl; 
    cout<<int(pow(26,2))<<endl; 
}

Results with doubles are weird.

double a=26; 
double b=2; 
cout<<int(pow(a,b))<<endl; #outputs 675 
cout<<int(pow(26.0,2.0))<<endl; # outputs 676 
cout<<int(pow(26*1.00,2*1.00))<<endl; # outputs 676