> In which country there is a cheap childcare, especially if we are talking about children under 3?

Norway. The maximum price for barnehage (kindergarten Norwegian style) is 1 200 NOK per month, about 120 USD, but never more than 6% of the household's income. Every child is guaranteed a place. Families with low income get 20 hours a week 'core time' free. Children can attend from one year old until they start school at five or six.

See https://www.statsforvalteren.no/innlandet/barnehage-og-oppla...