Some identities for multiple zeta values

In this note, we obtain the following identities,∑a+b+c=nζ(2a,2b,2c)=58ζ(2n)−14ζ(2)ζ(2n−2),for n>2,∑a+b+c+d=nζ(2a,2b,2c,2d)=3564ζ(2n)−516ζ(2)ζ(2n−2),for n>3. Meanwhile, some weighted version of sum formulas are also obtained.