Sun's Series via Cyclotomic Multiple Zeta Values

We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun’s series and their analogs can be represented as cyclotomic multiple zeta values of levels $N\in \{4,8,12,16,24\}$, namely Goncharov’s multiple polylogarithms evaluated at $N$-th roots of unity.