  In this paper, we first introduce a quantum $n$-space with a cocommutative
Hopf algebra structure. Then it is shown that to this quantum $n$-space there
corresponds a derivation algebra of $\sigma$-twisted derivations related to
some algebra automorphisms $\sigma$ on the quantum $n$-space. Furthermore, we
show that this derivation algebra is a noncommutative and non-cocommutative
Hopf algebra, namely, a quantum group. Morever, for this the quantum $n$-space,
we show how to construct a bicovariant differential calculus related to the
derivation algebra.
