Two parametric q-supercongruences from a summation formula for q-series

With the help of a summation formula for $q$-series and the creative microscoping method, we shall establish two parametric $q$-supercongruences. They are both modulo the third power of a cyclotomic polynomial. When $q\to 1$, one of them is able to engender the following conclusion: for any prime $p\equiv 2(\mathrm{m}\mathrm{o}\mathrm{d}3)$ and any nonnegative integer $s$ subject to $s\le (p-2)\mathrm{/}3$, $$\sum _{k=s}^{(p+1)\mathrm{/}3+s}(6k-1)\frac{(-\frac{1}{3}{)}_{k-s}(-\frac{1}{3}{)}_{k+s}(-\frac{1}{3}{)}_k}{(k-s)!(k+s)!k!}\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{p}^3)\mathrm{.}$$