Den Männern vs Die Männer

Question

So I am reading a grammar book, and there are a couple of tables which seem to contradict.

One table states: "The plural forms of the definite article are the same for all genders," and proceeds to show me:

Definite article + plural noun: Die Männer = The Men

Further down the same page, there is a table which states: "The forms of the definite article in each case are as follows" and shows:

Nominative: die
Accusative: die
Genitive: der
Dative: den

With an example:

Ich will nicht nur mit den Männern arbeiten.

I am confused! Could someone explain the difference between die Männer and den Männern?

Answer 1

You are mixing up two different things. (Without an actual quote I can’t determine whether the book is imprecise or you misunderstood.)

1. The definitive article has different forms for the cases, i.e. Nominative, Genitive, etc.
2. Unlike for singular, the definitive article plural is identical for masculine, feminine and neuter.

So:

Nominative:
- der Schuh, die Birne and das Ziel
- die Schuhe / Birnen / Ziele

Genitive:
- des Schuhs, der Birne and des Ziels
- der Schuhe / Birnen / Ziele

Dative:
- dem Schuh, der Birne and dem Ziel
- den Schuhen / Birnen / Zielen

Accusative:
- den Schuh, die Birne and das Ziel
- die Schuhe / Birnen / Ziele

Answer 2

One table states: "The plural forms of the definite article are the same for all genders"...

They mean "In the plural of the definite article, Plural Male Nominative = Female Nominative = Neuter Nominative". They don't mean "Plural Nominative = Accusative = Genitive = Dative", which is obviously not the case.

and proceeds to show me:

Definite article + plural noun: Die Männer = The Men

Yes, that's referring to the Nominative (not the other cases)

The second table is about the declination of the definite article / all cases of the plural, and the example:

Ich will nicht nur mit den Männern arbeiten.

is an example of Dative case