There are two words which are found in dictionaries in that meaning in Korea.
1) 좋다 : an adjective (usage : (~이/가/은/는) 좋다)
2) 좋아하다 : a transive verb(usage : (~을/를) 좋아하다)
In conversation they conjugate depending on the situation, the mood, politeness levels or tenses.
The both phrases you put as example should be "좋아하다" and "좋은데요" respectively.
The base form of "좋은데요" with '-요' can be 1) which makes 1) polite a bit.
a.좋다(a base form)
b.좋+아(informal, quite casual)
c.좋아+요(informal, but polite a bit)
d.좋은데요(infomal, but polite a bit)
e.좋습니다(formal and polite)
For example,
Most of Korean foods are hot, but they are delicious.
a. 대부분의 한국음식은 맵지만 맛이 매우 좋다.(just description)
b. 대부분의 한국음식은 맵지만 맛이 매우 좋아.(among friends)
c. 대부분의 한국음식은 맵지만 맛이 매우 좋아요.(polite a bit)
d. 대부분의 한국음식은 맵지만 맛이 매우 좋은데요.
(you just tasted it, I guess and indicates more personal preference with '-데')
e. 대부분의 한국음식은 맵지만 맛이 매우 좋습니다.(genenal description)
As for "좋아해요", its base form is "좋아하다" which a transitive verb.
a.좋아하다
b.좋아해
c.좋아해요
d.좋아합니다.
For instance,
I like Korean food.
a.나는 한국 음식을 좋아한다.(just description)
b.난 한국 음식을 좋아해(among friends)
c.저는 한국 음식을 좋아해요.(polite a bit with '저는' and '-요')
d.저는 한국 음식을 좋아합니다.(more polite than "c" and formal)
^_______^