Question 157
Prove that there exist infinitely many natural numbers $n$ with the following properties: we can represent number $n$ as a sum $n = a^2 + b^2$, and a sum $n = c^3 + d^3$, and can't represent it as a sum $n = x^6 + y^6$, where $a,b,c,d,x,y$ natural numbers.