$1\mathrm{.}3$ The $4$ giga$-$byte $(GB={10}^9$ bytes$)$ flash memory chip for an MP$3$ player is $32mm$ by $24mm$ by $2\mathrm{.}1mm.$ This memory chip holds $1000$ three$-$minute songs.

a$)$ How many seconds of music fit into a cube whose sides are $1mm?$

b$)$ How many bytes of memory are stored in a cube whose sides are $100m?$