Tensorial notations are helpful here as an alternative--and an excellent way to prove-- vector calculus identities mentionned in other answers (if you can't remember them of the top of your head). The Navier-Stokes equations for the i-th component of $v$ are:
$$ \partial_t v_i + \sum_{1\le j \le 3}v_j \partial_j v_i = -\partial_i p + \sum_{1\le j \le 3}\partial_j\partial_j v_i$$
where I use the shorthand notations $\partial_t=\frac{\partial}{\partial t}$ and $\partial_i = \frac{\partial}{\partial x_i}$.
Incompressibility is:
$$ \sum_{1\le j \le 3}\partial_j v_j = 0$$
Now let us use this notation to explicit the i-th component of the term in red:
$$ \left\{\boldsymbol{\nabla \cdot }( \boldsymbol{vv}) \right\}_i =\boldsymbol{\nabla \cdot }(v_i \boldsymbol{v})= \sum_{1\le j \le 3} \partial_j\left( v_i v_j\right) $$
We can distribute the derivative, and use imcompressibility:
$$ \left\{\boldsymbol{\nabla \cdot }( \boldsymbol{vv}) \right\}_i =v_i \underbrace{\sum_{1\le j \le 3} \partial_j v_j}_{=0} + \sum_{1\le j \le 3}v_j \partial_j v_i = \boldsymbol{v \cdot\nabla} v_i$$
This is how, for incompressible flows, advection can be written in these two different (but equivalent) forms. Written as a divergence, energy budgets over control volumes are then easily derived.