The cubic Borwein sign-pattern conjecture

Let $n$ be a positive integer, and define

$$P_n(q):=(1-q)(1-q^2)(1-q^4)(1-q^5)\cdots(1-q^{3n-2})(1-q^{3n-1}).$$

Cubic Borwein conjecture. The sign pattern of the coefficients in the expansion of $P_n(q)^3$ is $+--+--+--\cdots$, with the same convention concerning zero coefficients as above. The source describes this as only partially proved.