New type series for powers of $π$

Motivated by Ramanujan-type series and Zeilberger-type series, in this paper we investigate two new types of series for powers of $π$. For example, we prove that $\sum_{k=0}^\infty(198k^2-425k+210)\frac{k^3\binom{2k}k^3}{4096^k}=-\frac1{21π}$ and $\sum_{k=0}^\infty\frac{198k^2-227k+47}{\binom{2k}k^3}=\frac{3264-4π^2}{63}.$ We also pose many conjectures in this new direction.

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