A player can spend energy cubes to buy Power cards or sweep only during their own turn.

This is supported by the following rules:

• Under the section "4. Buy power Cards" (page 6), it states:
  "You now may buy one or more of the three face-up cards. To buy a Power card, spend as many [energy cubes] as the cost indicated at the top of the card. ... As long as you have enough [energy cubes], you can continue to buy and/or sweep cards."

• The Turn Overview (page 4) lists "4. Buy Power Cards" as a step in the turn sequence, which occurs after resolving dice and before ending the turn.

There is no mention in the provided context of being able to buy or sweep Power cards outside of your own turn.

Source: pages 4 and 6.

Source: Core Rulebook (pp. 2, 3, 4, 6)