IR-TST 2007 Problem 10

Find all polynomials of degree 3, such that for each $x,y\geq 0$ : $p(x+y)\geq p(x)+p(y)$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.