The ULN2003 has an absolute max switch current of 500mA for ONE pin. Not all seven.
Absolute total max for seven is 2.5A, but you can't reach that because of dissipation limits (chip temp).
It seems you have connected 23-25 LEDs in parallel to one pin. That would explain your current requirements.
Can't you connect the LEDs in series, and use a supply with a higher voltage.
Post a circuit diagram.
Leo..