Can a creature with double strike deal damage in both the first strike and regular damage steps when unblocked?

Double strike (CR 702.4) grants a creature the ability to deal combat damage in both the first strike combat damage step and the regular combat damage step. This applies whether the creature is blocked or unblocked.

During combat, if any creature has first strike or double strike, a first strike combat damage step occurs before the regular combat damage step (CR 702.2b, 702.4b). An unblocked creature with double strike deals its power in damage to the defending player (or planeswalker it was attacking) in the first strike step, and then deals its power in damage again in the regular damage step (CR 509.2).

It is important to note that the creature is not 'dealing damage twice at once' — these are two separate damage steps, meaning any effects that trigger on combat damage will trigger separately in each step. Lifelink, infect, and similar abilities all apply to both instances of damage independently.

For example: You attack with a 3/3 creature with double strike that is unblocked. In the first strike combat damage step it deals 3 damage to your opponent. Then, in the regular combat damage step, it deals another 3 damage to your opponent — for a total of 6 damage dealt across two separate steps.

This is because CR 702.4b states that double strike means the creature 'assigns combat damage twice,' once in each damage step, giving unblocked double strikers a unique ability to deal effectively double their power in damage each attack.