Question 160
A polynomial $P(x)$ with integer coefficients is called cube-represented if it can be represented as the sum of several cubes of polynomials with integer coefficients.
Example: $3x + 3x^{2}$ is cube-represented because $3x + 3x^{2} = (x+1)^{3} + (-x)^{3} + (-1)^{3}$.
1. Is $3x^{2}$ a cube-represented polynomial?
2. How many quadratic polynomials $P(x)$ with integer coefficients belonging to the set $\{1,2,3, \ldots, 2017\}$ are cube-represented?
Example: $3x + 3x^{2}$ is cube-represented because $3x + 3x^{2} = (x+1)^{3} + (-x)^{3} + (-1)^{3}$.
1. Is $3x^{2}$ a cube-represented polynomial?
2. How many quadratic polynomials $P(x)$ with integer coefficients belonging to the set $\{1,2,3, \ldots, 2017\}$ are cube-represented?