Prism dice probability

[jokez]

Emma makes a straight prism with an equilateral triangle as its base from a net labeled as shown in the adjacent figure. She uses the prism as a 'thrower, where the letter at the bottom is considered to be rolled.
Show: If the probability of rolling M A T H E is greater than the probability of rolling EM M A, then the probability of rolling T E E is greater than 1/64
Note: Rolling M A T H E means, if the die is rolled five times in this order, rolling the
M. A, T H, and E to be rolled. Similarly, "E M M A roll" and "T E E roll" are for four and four times respectively.

[Genady]

I think it boils down to this:

3a+2b=1

a²>b

Show that 

a³>1/64