I don't normally do people's homework, but you've given it a shot, most people just ask us to do it. You've made two mistakes:
1 - you emit a newline after every *, you need to emit a newline after each group of *s
2 - you don't reset colum to 0, so your rows never get any bigger.
I recommend learning to use your debugger, that should have helped you find both of these issues. I don't know what compiler you're using, but they all suppor breakpoints AFAIK.
using namespace std;
int n = 5;
int row = 0;
int colum = 0;
cout << "*";
cout << "\n";
colum = 0;