One year ago, the number of years in Jane's age was a perfect square, and one year from now, her age will be a perfect cube. How many years old is Jane?
Let's consider a few small perfect cubes to see two less which is a perfect square: $2^3-2=6$, not a perfect square; $3^3-2=25=5^2$. Thus Jane is $27-1=\boxed{26}$ years old.