What's got this poem's speaker so worked up? There are a lot of possible answers, but he does seem pretty hung up on the notion that—by heading overseas to teach the world a lesson—these white men will be gaining valuable experience. In other words, they'll be maturing, growing up, becoming Men with a capital M. It's time to put away the Tinker Toys and the Xbox, apparently.
Line 3: At the start of the poem, the speaker sets his sights on the "sons" as the ones who will be responsible for going on this civilizing mission. We can read this word choice as a figurative way of calling out the younger generation of white men, who would be somewhere between carefree adolescence and serious adulthood.
Line 50: Our speaker's "Grow up and be a man" speech reaches its most energetic heights in the final stanza. In this line he says outright that it's time for the White Man to move on from the figurative "childish days" of his youth.
Line 53: "You can act like a man!" says Don Vito Corleone in a famous scene in The Godfather. With this "search your manhood" metaphor, our speaker's saying essentially the same thing here. By going through all the hardship of "civilizing" the rest of the world, these white men will have truly come into their manhood.