Each LED will consume an amount of power equal to its forward voltage drop at whatever current is passing through the LED. If you connect LEDs in parallel, there is no way to guarantee that each will have the same forward voltage drop, nor that the current will distribute equally across all the LEDs connected in parallel.
If you want to connect LEDs "in parallel" place a current-limiting resistor in series with each LED, then wire as many of these resistor/LED series combinations in parallel with each other as desired. Again, the power dissipated will be the forward voltage drop across a given LED multiplied by the current through that LED.
You do the math. Relying on "glittering generalizations" such as "leds in series consume less power" will only mislead you, and such statements serve no useful purpose. Learn about electricity, Ohm's Law, Kirchoff's Current and Voltage Laws so you can participate meaningfully on this forum.