Historical path leading to the widespread adoption of sugar cultivation in americas:

The first historical record associates the beginning of sugar in the Americas with Christopher Columbus' initial and epic voyage of the discovery of the New World in 1492.

The sugar cane plant is native to Southeast Asia and in Europe had already created an appetite for more through the Eastern trade routes. These were of course difficult routes that included trade caravans over land and water to reach Asia from Europe.

With Columbus the initial planting of sugar cane occurred in the Dominican Republic. The Caribbean islands maintain a perfect tropical climate for the plant and as such, flourished. Other colonizers, like the British, Portuguese and French soon followed suit within their own colonies spread throughout the New World. 

The Portuguese had transplanted or moved some of the seedlings, or small plants from the Dominican into Brazil and other areas of their colonized lands. In fact, Brazil is the largest producer of sugar cane in the world today.

The desire for more sugar during this early settlement, led to a "triangle of trade". In order to satisfy the need for production of sugar, ships sailed to the western coasts of Africa to bring slaves to work the sugar plantations. After depositing the slaves, the ships would pick up sugar and rum, an alcohol created from sugar, and bring these goods back to the European powers. This completed the cycle for the ships, which would then return to Africa to gather more slaves.

By 1505, this trade route was set up and going strong. And for the next 300 years or so, would remain in effect.