When I execute the following command, I get a numerical output as follows:
In[28]:= Maximize[{n^3, n^3 <= 3110400000000}, n, Integers]
Out[28]= {3110217954173, {n -> 14597}}
But if I change the function to maximise as follows:
In[30]:= Maximize[{n^2, n^2 <= 3110400000000}, n, Integers]
Out[30]= Maximize[{n^2, n^2 <= 3110400000000}, n, Integers]
Why do I not get an answer for $n$ in the latter case?