Some identities for multiple zeta values

Abstract In this note, we obtain the following identities, ∑ a + b + c = n ζ ( 2 a , 2 b , 2 c ) = 5 8 ζ ( 2 n ) − 1 4 ζ ( 2 ) ζ ( 2 n − 2 ) , for n > 2 , ∑ a + b + c + d = n ζ ( 2 a , 2 b , 2 c , 2 d ) = 35 64 ζ ( 2 n ) − 5 16 ζ ( 2 ) ζ ( 2 n − 2 ) , for n > 3 . Meanwhile, some weighted version of sum formulas are also obtained.