This is the 940th most frequent German word.
großer
"Großer" means "bigger" or "greater" in English.
'großer' (modified as 'großen') is used here as an adjective modifying the noun 'Hund', and it reflects the gender, number, and case of the noun it describes in the accusative singular masculine form.
Er hat einen großen Hund.
He has a big dog.
'großer' is an adjective modifying the noun 'Erfolg', used in the nominative singular masculine form.
Das ist ein großer Erfolg.
That is a great success.
'großer' (modified as 'großen') acts as an adjective describing the noun 'Künstlers' (artist) in the masculine singular genitive case.