Kurtz may enjoy cutting off heads, but he's a man of many interests. Poetry is apparently one of his passions.

Kipling's "If"

In one of the American photojournalist's babbling speeches, he tells Willard:

PHOTOJOURNALIST: Hey, man, you don't talk to the Colonel. You listen to him. The man's enlarged my mind. He's a poet warrior in the classic sense. I mean sometimes he'll...uh...well, you'll say "hello" to him, right? And he'll just walk right by you. He won't even notice you. And suddenly he'll grab you, and he'll throw you in a corner, and he'll say, "Do you know that 'if' is the middle word in life? 'If you can keep your head when all about you are losing theirs and blaming it on you, if you can trust yourself when all men doubt you'"...I mean I'm...no, I can't...I'm a little man, I'm a little man, he's...he's a great man! "I should have been a pair of ragged claws scuttling across the floors of silent seas..."

The lines "If you can keep your head when all about you are losing theirs and blaming it on you / If you can trust yourself when all men doubt you" are from a famous Rudyard Kipling poem entitled "If." The poem's basically an evocation of the kind of hardcore, tough, stoic individual Col. Kurtz wants to be, containing lines like these:

If you can force your heart and nerve and sinew
To serve your turn long after they are gone,
And so hold on when there is nothing in you
Except the Will which says to them: "Hold on!"

Kurtz is all about that kind of intense willpower and personal fortitude. It's what he thinks the American leadership in Vietnam is lacking.

T.S. Eliot's "The Hollow Men" and "The Love Song of J. Alfred Prufrock"

Kurtz loves dark, emo poetry. How else is he going to express his tormented soul?

He reads lines from T.S. Eliot's poem "The Hollow Men" as Willard and the photojournalist sit nearby:

KURTZ: We are the hollow men
We are the stuffed men
Leaning together
Headpiece filled with straw.
Alas! Our dried voices, when
We whisper together
Are quiet and meaningless
As wind in dry grass
Or rats' feet over broken glass
In our dry cellar Shape without form, shade without color,
Paralysed force, gesture without motion…

Kurtz is probably thinking that these "hollow men" are the American leadership, the confused people, empty of reason, who sent him into combat and now want to kill him for doing what they asked him to do. Kurtz has been hollowed out, too, by all the brutality he's witnessed.

Fun Fact: the epigraph at the beginning of "The Hollow Men" reads: "Mistah Kurtz—he dead." This is like looking into an infinite hall of mirrors; we're watching a film based on Heart of Darkness in which Kurtz is reading a poem with an epigraph taken from Heart of Darkness about a man named Kurtz.

The photojournalist earlier quotes another line from Eliot.

PHOTOJOURNALIST: I should have been a pair of ragged claws scuttling across the floors of silent seas…

This comes from the "The Love Song of J. Alfred Prufrock." It's one of the bleakest, most despairing lines in literature. In other words, just perfect for this film.