Learn Hardcore French: Nous n’avons aucun sucre; prends du miel.

Ne … aucun(e) means “not a single, absolutely no.” It’s a bit stronger and a touch more formal: Nous n’avons aucun sucre. (We have absolutely no sugar.)
Ne … pas de is the neutral, most common way to say “no/any”: Nous n’avons pas de sucre. (We don’t have any sugar.)

Avoid doubling them: in standard French you don’t say Je n’ai pas aucun sucre. If you want extra emphasis, use alternatives like Je n’ai pas le moindre sucre or Je n’ai pas un seul gramme de sucre.

Does aucun agree with the noun? Why not aucune?

Yes. Aucun is a determiner that agrees in gender (and, in rare cases, number) with the noun:

Masculine singular: aucun sucre
Feminine singular: aucune farine, aucune idée
Rare plural (only with nouns that are normally plural): aucuns frais, aucunes funérailles

Since sucre is masculine, you use aucun sucre.

Why is aucun followed by a singular noun if “sugar” is uncountable?

With aucun(e), French uses the singular even for mass/uncountable nouns. So you say aucun sucre, aucune eau, aucune viande, etc.

Why isn’t there a de before aucun (why not n’avons d’aucun sucre)?

Because aucun itself is the determiner of the noun; you don’t add de unless the verb or adjective itself requires de.

Correct here: Nous n’avons aucun sucre. (The verb avoir doesn’t take de.)
With a verb that needs de: Je ne me souviens d’aucun détail. (Because se souvenir de requires de.)

Why is it prends and not prend?

It’s the imperative (a command) addressed to one person (tu).

Present tense: tu prends, il prend
Imperative: prends (2nd person singular), prenons (1st plural), prenez (2nd plural/polite) So the command is Prends du miel. The final -s is normal here; it’s not the 3rd-person form prend.

How do I make the command polite or address several people?

Use the vous imperative: Prenez du miel.
To make a friendly suggestion including yourself: Prenons du miel.

What does du mean in du miel, and why is it needed?

Du is the partitive article (de + le). It usually translates as “some” and is used with mass nouns when you mean an unspecified amount. In French you normally need an article before a noun, so you can’t just say “take honey” without it; you say Prends du miel.

When would it be de l’ instead of du?

Before a vowel or silent h, de + le/la becomes de l’:

de l’eau, de l’ail, de l’argent Here, miel starts with a consonant sound, so it’s du miel. For a feminine mass noun with consonant: de la confiture.

What happens to du miel under negation?

With a standard negation, partitive and indefinite articles usually become de:

Je n’ai pas de miel. Be careful: pas du miel is used only when you negate a specific/definite reference or a classification (e.g., Ce n’est pas du miel = “This isn’t honey”).

Could I say Prends le miel instead? What’s the difference?

Prends du miel = “Have some honey” (an unspecified amount; general suggestion).
Prends le miel = “Take the honey” (the specific honey we both know about, e.g., the jar on the table). “Sugars” in the plural exists in specialized contexts (varieties, sugar cubes), but Prends des miels would be odd; you might hear goûter différents miels (“taste different honeys”) in a gourmet context.

How do I replace du miel with a pronoun?

Use en for quantities introduced by de. In the affirmative imperative, attach it with hyphens:

Prends-en. (Take some.) Note: the -s in prends stays (and is pronounced) before en/y: Prends-en, Prends-y.

Is the semicolon (;) normal here? Could I use something else?

Yes. The semicolon links two closely related independent clauses: Nous n’avons aucun sucre; prends du miel.
Alternatives:

Period: Nous n’avons aucun sucre. Prends du miel.
Comma with a connector: Nous n’avons aucun sucre, alors/préférablement prends du miel. Typographic note: in French publishing, a (thin, non‑breaking) space is placed before ;, but in everyday typing people often omit it.

Any pronunciation tips or liaisons to watch?

Nous n’avons: typically [nu navɔ̃]; there’s no liaison from nous to avons because ne sits in between. Without ne (in speech), Nous avons is [nuz‿avɔ̃] with liaison.
aucun: [okœ̃] (nasal vowel at the end).
sucre: [sykʁ] (roll/uvular r at the end).
prends: [pʁɑ̃] (final -s silent unless followed by en/y).
du miel: [dy mjɛl].

Is nous the most natural choice, or would on sound better?

In everyday speech, on is more common than nous for “we.” A very natural spoken version would be:

On n’a pas de sucre; prends du miel.
If you keep aucun: On n’a aucun sucre; prends du miel.