Let's start by listening to Langston Hughes himself reading the poem : Mulatto
To put things in perspective, and within the context of Black Lives Matter, you could also listen to this 1967 conference recorded at UCLA. (You can jump to 9:37 if you want to skip the introduction).
And regarding his life, and the Harlem Renaissance more broadly, here's a twofer, Alice Walker about Langston Hughes.
Hughes was very much influenced by music, especially the blues, and many of his poems read as lyrics. In preparing for your close reading of 'Mulatto', therefore, pay especial attention to sounds and rhythm.