It is said that the spark core uses (at the spark home page)
100mA typical current consumption; 300mA peak consumption (during transmit events)
I need something small to power up the core, is it possible to use this converter or this maybe? (from the mains)
@gcats, the CC3000 can peak at 350ma so I would recommend a larger supply. The “converter” you link to requires external components while the second item supplies 15V.
I could go with something like this. Or, just use any small AC USB power cube. 
How about this one?
http://www.digikey.com/product-detail/en/RAC03-05SC%2F277/945-1662-5-ND/3593402
@gcats, looks good! Of course, it’s a lot pricier but more industrial also.