  We construct the well-known decomposition of the Lie algebra $\mathfrak{e}_8$
into representations of $\mathfrak{e}_6\oplus\mathfrak{su}(3)$ using explicit
matrix representations over pairs of division algebras. The minimal
representation of $\mathfrak{e}_6$, namely the Albert algebra, is thus realized
explicitly within $\mathfrak{e}_8$, with the action given by the matrix
commutator in $\mathfrak{e}_8$, and with a natural parameterization using
division algebras. Each resulting copy of the Albert algebra consists of
anti-Hermitian matrices in $\mathfrak{e}_8$, labeled by imaginary (split)
octonions. Our formalism naturally extends from the Lie algebra to the Lie
group $E_6\subset E_8$.
