Most nouns that are masculine and end in -e in their nominative singular form are called weak nouns, or schwache Substantive. Since most German nouns ending in -e are feminine, these exceptions are easy to recognize. There are, however, also weak nouns that don't end in -e in the nominative singular form, and these are harder to recognize. Many of these words are very similar to their English equivalents and relate to professions or politics. They can often be recognized by the fact that they end in -ant or -ist.
What sets them apart from other nouns is the fact that in all cases except for nominative, they end in -en or -n.
Here's an example of the weak noun der Präsident with the -en ending in the singular dative case:
... und hab' auch mit dem französischen Präsidenten darüber gesprochen.
... and I've also talked to the French President about this.
Caption 68, Angela Merkel - beim NachhaltigkeitsratPlay Caption
And the weak noun der Elefant in the singular accusative case:
Frederick, zeig mir einen Elefanten!
Frederick, show me an elephant!
Caption 3, Piggeldy und Frederick - Der ElefantPlay Caption
And finally, der Mensch in the singular genitive case:
Die Würde des Menschen ist unantastbar.
The dignity of a human being is inviolable.
Caption 38, Integration von Nationalitäten - Hessen miteinanderPlay Caption
Visit this page to see more examples of weak nouns, and visit Yabla German to find more examples of weak masculine nouns in practice.