Is a three dB difference in sound twice as loud?

No, 10 dB is perceived to be twice as loud, and requires 10 times the power.

Doubling of the volume (loudness) should be perceived by a level difference of 10 dB − psychoacousticians say.

Doubling the sound pressure (voltage) level corresponds to a measured level change of 6 dB.

Doubling of acoustic power (sound intensity) level corresponds to a calculated level change of 3 dB.

Scroll down to related links and look at "How many decibels (dB) is twice (double, half) or three times as loud?"