Is a resistor needed for LEDs in this beatbox project?
Yes you need a resister per LED. Assuming you want your LEDs to run at a current of about \$I_f\$ = 20mA current and your LEDs have a forward voltage of \$V_f\$ = 1.7V (this is a wild guess, check your datasheet), you'll want to size your resistors as follows:

\$ (12 - V_f) / (I_f) = R\$

So for the parameters I suggested that would be (12 - 1.7) / (0.020) = 515 ohms, and you would just pick a "common" (e.g. E12 series) resistor that is larger than that, so 560 ohms is your best bet. I gave you the equation form so you can plug in appropriate values from your datasheet, and obviously the 12 in the equation is your supply voltage. Keep in mind that the power your resistor will need to dissipate is:

\$P = I_f * I_f * R\$

So in this case 0.02 * 0.02 * 560 = 0.224 Watts, so definitely get 1/4W resistors, not 1/8W resistors.