  In this paper, we give an elementary account into Zagier's formula for
multiple zeta values involving Hoffman elements. Our approach allows us to
obtain direct proof in a special case via rational zeta series involving the
coefficient $\zeta(2n)$. This formula plays an important role in proving
Hoffman's conjecture which asserts that every multiple zeta value of weight $k$
can be expressed as a $\mathbb{Q}$-linear combinations of multiple zeta values
of the same weight involving $2$'s and $3$'s. Also, using a similar
hypergeometric argument via rational zeta series, we produce a new Zagier-type
formula for the multiple special Hurwitz zeta values.
