Is there a way to dissolve more sugar into a solution that it should hold at that temperature? Explain how this is done and what the solution would be called.

The answer is: supersaturated solution.

A supersaturated solution contains more of the dissolved substance than could be dissolved by the solvent under normal circumstances.

A way to dissolve more sugar into a solution is heating a solution.

The more heat is added to a system, the more soluble a substance (in this example sugar) becomes.

The solution will become supersaturated if this solution is suddenly cooled at a rate faster than the rate of precipitation.