Germany as a nation never colonized the Americas. Why? Because the modern nation of Germany did not exist until the 19th century, first with the German Federation, and form 1871, the German Empire. By then all of America was already independent former colonies.

Now some of the German duchies and principalities did have shortlived colonies in the Americas in the Early Modern Period. Most significant was Klein-Venedig colony from 1528 to 1546. Basically, the banking family of the Welsers from the free city of Augsburg was granted Venezuela as a guarantee by the Spanish King Charles V, in return for extending the loans he needed to become Holy Roman Emperor. For 18 years Venezuela was colonized and developed by the Germans, and various German explorers like Georg Hohermuth von Speyer, Nikolaus Federman and Ambrosius Ehinger travelled throughout northern SOuth America. The loanw as eventually cancelled though.

In the 17th Century, the strongest German state, Brandenburg, made a short-lived attempt at making a trans-atlantic colonial empire. It acquired trading posts in Africa, as well as the islands of St. Thomas, leased from Denmark, and Crab Island in the Caribbean. In 1693 the colony was seized by the Danes however, and the African colonies later sold to the Dutch.

Finally, the Duchy of Courland in modern Lativa, a vassal state of Poland-Lithuania, but led by Baltic Germans, also had a short-lived attempt to colonize Tobago in the Caribbean, but they did not have sufficient strength to protect the colony from the Dutch, and eventually it was given up. After 1693, no German possessions in America was intact.

Imperial Germany in the late 19th century did found global colonies. In West- and East Africa they founded big colonies. They also colonized New Guinea and the Pacific Islands, and the Qingdao Enclave in China, but all this was lost in WWI.

It is worth noting there was one example of German interest in colonizing a part of hte Americas in the Imperial Era. By 1907 Germany did actually approach Denmark for the chance to take over the Danish West Indies (St. Croix, St. Jan and St. Thomas) to gain a naval base in the Caribbean, at least it was considered by Denmark as an agreement in exchange for respecting Danish neutrality in case of a war (The West Indies had been offered to Prussia in 1864 in exchange for keeping Northern Schleswig after Denmark had lost a war, but this was rejected by Prussia).

In the end nothing came of the German interest in the Danish West Indies, but the fear of Germany acquiring the islands was the primary motivation for the American purchase of the islands in 1917, turning them into the US Virgin Islands.

As for why the German states never colonized the Americas, the answer lies in the facts above. Colonization was not easy. Many smaller European states attempted it, but did not have sufficient strength to back it up and successfully defend the colonies. The German states were not natural seafaring states with their own strong navy - despite their position near the Baltic, Brandenburg and later Prussia would have a pretty much non-existent navy until the late 19th century. Given these structural issues, colonization became practically impossible, and the German states also remained much more committed to concerns on the European continent than abroad. This attitude lasted all the way up to Bismarck, who thought colonization was a distraction.