$\newcommand{\Cov}{\operatorname{Cov}}$
$X_i$ from $i=1,\ldots,n$ is a set of random variables
The following confuses me:
$\Cov\left(\sum_{i=1}^n X_i, \sum_{j=1}^n X_j\right) =$ the sum of all possible covariance pairs (so $n\cdot n$ terms) (source is the book I'm currently reading)
In my thoughts, the expansion might as well be
$$\Cov(X_1, X_1)+\Cov(X_2, X_2)+\cdots+\Cov(X_n, X_n)$$
Or
$$\Cov(X_1 + X_2 + \cdots +X_n, X_1 + X_2 + \cdots +X_n)$$