In American English, the spelling is data center or datacenter, and in British English, it is data centre. This simply follows how the word center/centre is spelled in the US and UK. This difference is also seen in word pairs such as theater/theatre and meter/metre.
Center/centre is both a noun and a verb, and the spelling remains consistent for those two word classes.
As a noun, center/centre can be a physical place (e.g., “London is a center/centre for dance and the arts”), a description of a mathematical point (e.g., “The center/centre of a circle”), or a figurative place (e.g., “From the day he was born, Hugo has always been at the center/centre of our world”).
The QuillBot Grammar Checker can ensure you are using the correct American or British English spelling of data center/centre.