Effect of function inequality on Big O notation

Question

Let $f(n) \ge n^6+3$: How does the inequality affect the Big O of f(n)? Because if I understand correctly, O(g) includes any function that is smaller or equal to g (where g(n) = c*n). But with an inequality, there is no 'upper bound' because f(n) could be anything above $n^6+3$. As a practical example, how would O(f) compare to say, Ω(f)?