I would mix up some pva glue and water,
and rip up (jagged edges are better than straight) some white paper into small bits, good fun
dip in the glue mix and cover the box over lapping the paper,
take the drawers out, do the fronts not the sides,
then you have white box to start with,
let it dry,
and either use tissue paper to paper over same method as before or cut pictures and words out of magazines,wallpaper, cards,buttons, beads, glitter, sequins finish with a coating of pva glue, it will last a life time.
or paint,
but poster painting with poster paints on brown is going to be murky.