Vector Spaces & Bases · Superchallenge problem

Let $V = \mathbb{F}_2^3$, where $\mathbb{F}_2 = \{0,1\}$ with arithmetic mod $2$. How many ordered pairs $(U, W)$ of subspaces of $V$ satisfy $U\oplus W = V$, that is, $U + W = V$ and $U\cap W = \{\mathbf 0\}$?