Let X, Y be vector spaces. It is shown that if an even mapping $f:X{ ightarrow}Y$ satisfies f(0) = 0, and $$2(_{2d-2}C_{d-1}-_{2d-2}C_d)f({sum_{j=1}^{2d}}x_j)+{sum_{{iota}(j)=0,1,{{smallsum}_{j=1}^{2d}}{iota}(j)=d}};f({sum_{j=1}^{2d}}(-1)^{{iota}(j)}x_j)=2(_{2d-1}C_d+_{2d-2}C_{d-1}-_{2d-2}C_d){sum_{j=1}^{2d}}f(x_j)$$ for all $x_1$, ${cdots}$, $x_{2d}{in}X$, then the even mapping $f:X{ ightarrow}Y$ is quadratic. Furthermore, we prove the Hyers-Ulam stability of the above functional equation in Banach spaces.