Have you run across the situation where one sentence ending with a colon is followed by another sentence? Do you capitalize the first word of that second sentence? Why would you use a colon between the two sentences rather than a period or a semicolon?
Rule for colons between sentences: Use a colon instead of a semicolon or a period between two sentences when the second sentence explains or illustrates something in the first sentence.
Capitalization rule with sentences after colons: If only one sentence follows the colon, do not capitalize the first word of the new sentence. If two or more sentences follow the colon, capitalize the first word of each sentence following.
Example: One of my favorite novels is by Kurt Vonnegut: his novel, Slaughterhouse-Five, is often funny, yet packs an emotional punch.
Example: Garlic is used generously in Italian dishes: It greatly enhances the flavor of pasta. Garlic also enhances the flavor of lasagna, one of my favorite dishes.
Now, should you capitalize the first word after a colon if it begins a list rather than a new sentence?
Rule for capitalizing with lists after colons: Do not capitalize the first word of a list after a colon.
Example: I like the following Italian dishes: pasta primavera, eggplant Parmesan, and lasagna. (Parmesan is capitalized because it comes from the Italian city of Parma.)
Source: Grammarbook