Final answer:
The method to break down a sugar cube into simpler substances is hydrolysis, which splits the sucrose into glucose and fructose with the addition of water. Methods like distillation, agitation, or fermentation do not produce the same chemical breakdown of the sugar into simpler sugars.
Step-by-step explanation:
The method that can break down the sugar in a sugar cube into simpler substances is hydrolysis. Hydrolysis involves the chemical breakdown of a compound due to reaction with water. When water is present, the sugar molecule can undergo a hydrolysis reaction whereby it is split into its monomer constituents, glucose and fructose. This is a catabolic process and an example of a chemical change that produces matter with a different composition.
Options like distillation and dissolving sugar in water involve physical changes that do not break down sugar into simpler substances. Distillation separates substances based on their volatile properties, but doesn't chemically alter the sugar. Agitation only increases the rate of dissolution, without breaking the molecular bonds within the sugar cube. Finally, combustion is a process where sugar would react with oxygen to produce carbon dioxide and water, a form of decomposition but not breaking down into simpler sugars. Fermentation, on the other hand, is a biological process that breaks sugars down into alcohol and carbon dioxide, but it's facilitated by microorganisms and not solely by water as in hydrolysis.