Upsampling PCM audio: from 6 kHz to 8kHz
If processing cost is not a problem, you may use the following algorithm for sample rate converting your data from 6 khz to 8 khz.

1- expand your signal x[n] by 8, producing xe[n] (insert 7 zeros after every sample of x[n])
2- design a low pass filter hlpf[n] with a gain of 8 and cutoff frequency pi/8
3- process the expanded signal with this lowpass filter = xef[n]
4- compress output of the filter by 6 via selecting every 6th sample: y[n]=xef[6n]
(NOTE: You can also do this with 4:3 upsample and down sample, with a new filter,  which would require less processing cost)

Lowpass filter must be sharp enough to ensure proper anti-aliazing. If this is too much overburden for  simple rate conversion then try high order polynomial resampling. That could also be costly however.