It’s easy to go to the grocery store and buy a bag of sugar.
At the time the travelers were heading west on the Oregon Trail, it was not at all easy to get sugar and to store it for the trip.
In Independence Missouri, there were stores that sold sugar. It was a good idea to buy enough for the trip. There was no guarantee that they could get sugar at the few places where supplies were sold along the way.
Sugar, at that time usually was sold in loaves. The loaves were cone shaped and solid.
You could break up the loaves at the store and put it through their grinder. I couldn’t find a picture off the loaf with a tool.
On the trail, what was easiest to use was taken along. After a long day of walking alongside of the wagons, people were in no mood to fuss around with complicated food preparation.

I found pictures of different forms of sugar. The white cone of sugar would not have been sold in the stores. The loaves would have been mostly brown with a bit of white. This was because sugar has to be refined and that is a process that takes time.
The estimated length of the trail is 2,170 miles. It took four to six months to get to the destination in Oregon.

I’ll start with a map of the trail from the National Park Service.

The following pictures are from Wikipedia Commons, except for the last one.

The first picture is of a sugar cane plant in a pot in Kew Gardens  by, Adrian Pingstone.

The next three pictures are of sugar loaves.

By, Petr Adam Dohnalek

By, User: FA 2010

By, User: FA2010

This is a picture of sugar cubes which are common now, but not back then.

By, carioca

The next four pictures are of the things that were used to break off pieces from the sugar loaf and make it ready for use.

These are sugar nips and were made of iron  by, Hamster62

This shows what they used  to break off a part of the loaf and then nip it into smaller pieces. By, s. o.

Sugar loaf box  by, Mr. Seasword

Another kind of sugar loaf box  by, Wolfgang Sauber

Let’s say that you have broken off pieces of sugar and want to grind them for baking. You could use a mortar and pestle.

By Evan-Amos

The next five pictures show different sugars ground up.

Raw cane sugar  by, Fritzs

Raw cane sugar, light  by, Fritzs

White cane sugar  by, Fritzs

Traditionally dried sugar  by, Fritzs

By, Romain Behar

Say you have the sugar ground. You need something to store the sugar in. One way would be to have small air and water tight barrels. This last picture was taken by, Petr Krachtovil, publicdomainpictures.